In contrast to the crude analog-digital
combinations of the 1960's, today's hybrids
are true multiprocessors supported by realtime operating systems. Their solid-state
analog computing elements loaded digitally
in microseconds, together with their
equation-oriented compilers, provide
efficient, automatic setup and high productivity. Teamed with flexible, low-cost
alphanumeric/graphic displays, modern
hybrids are being applied over the full
spectrum of scientific and engineering
studies. Since the average hybrid system
has an equivalent digital processing speed
of over 10 million operations per second,
at less than one-tenth the cost of large
digital data processors, typical users
realize cost savings of over 100/1.
m
Hybrid Digital/Analog
Computer Systems
J. Paul Landauer
Electronic Associates, Inc.
Introduction
Third-generation hybrid computing systems provide the speed and versatility essential for a broad
range of scientific/engineering applications in
industry, government, and education. The modern
hybrid computer is a digitally based system utilizing
a low-cost, high-speed CPU to control and augment
parallel analog processors. In addition, external
machines can be used to program the analog processor and may be interfaced to the hybrid system
to provide additional digital computer capacity.
In contrast to earlier analog computers, parallel
processors are designed specifically for digital computer operation, including all-solid-state computing
blocks which can be set up automatically in microseconds. Today's hybrids include significant improvements over earlier analog and hybrid computers
in both hardware and software to simplify programming, increase speed and productivity, enhance graphical interaction/documentation, and
extend the classes of application. Through the use
of MSI digital circuits, IC and thick film linear
technology, and the latest graphic terminals, these
extended capabilities are provided at a lower cost
than was possible with earlier hybrids.
July 1976
This paper first describes the rationale of hybrid
computation versus other alternative computing
technologies. The structure and characteristics of
modern systems are then discussed, including the
unique, real-time operating systems. Finally, a number of specific hybrid computer applications are
outlined to demonstrate the versatility which these
systems offer for the efficient solution of scientific
and engineering problems.
Hybrid computationidata processing
With the wide range of electronic data processing equipment available on either a dedicated or
remote-access basis, one may ask why hybrid computation should be considered at all. To appreciate
the answer to this question, it is essential to realize
how computers are used for scientific and engineering
studies. A typical study (see Figure 1) is usually
initiated by a concept-for example, to develop or
improve an existing process or device. This usually
leads in two directions: a mathematical description
of the concept and experimental testing. If the
base of knowledge is not sufficient to formulate
the concept mathematically, it is very difficult
15
-7
-
- -- ------"
NO
Figure 1. Scientific analysis/design study
if not impossible to continue the study, and the
concept is then likely to be stored or discarded.
Experimental testing of the concept is also required
in most cases to obtain parameters for the mathematical model and to verify cortputed results.
Validation of the mathematical model is usually
an iterative procedure since the model must often
be changed to sufficiently match experimental
results. The study then enters the most important
phase, during which the investigator gains insight
into the operational characteristics of the process
or device. This usually requires a kind of conversation between the engineer/scientist and the mathematical formulation. He must understand the stability
of the system, sensitivity of parameters, and perhaps
develop control schemes to handle unforeseen extreme operating conditions. Extensions of the
mathematical model may be required to handle
these new aspects of the system, and, in fact,
the model may become simplified as the physical
system is better understood. Finally, the study
enters its last phase-design optimization. Here one
selects the significant design parameters to meet
specified technical criteria such as overshoot, damping, safety, etc., or business criteria such as yield,
cost, or ease of manufacture. Usually at this stage
a prototype of the device or a pilot plant of the
process is implemented. The device or process may
be interfaced to the environmental portion of the
computer model so that the final optimum design
is tested as its design is changed.
Except for trivial physical systems, a computer
is essential to perform all phases in the scientific
study. It can often be used to control and monitor
the experimental testing needed to acquire the
necessary data for the various phases of the study.
The most comprehensive and valuable mathematical
models should represent the dynamics of the system
16
under study where the steady state is just a particular solution. Therefore, the computer must solve
either ordinary differential or partial differential
equations for each phase.
With this foundation, the original question can
be answered. Basically, there are four main reasons
for the present widespread use of hybrid computation: (1) speed/elapsed time, (2) cost, (3) real-time/
hardware interface, and (4) conversational analysis.
The low end of the line is about as fast
as the largest commercial scientific digital
computers, and at the-upper end there is
presently no equivalent EDP capability
at any price.
If
we assume
that equivalent computing is done
at the same accuracy, the speed of modern hybrid
systems ranges from 1 to 150 MIPS (million instruc-
tions per second) for typical engineering design
studies.' That is, the low end of the line is about
as fast as the largest commercial scientific digital
computers, and at the upper end there is presently
no equivalent EDP capability at any price. This
speed means that the engineer or scientist can
investigate a much wider range of conditions in
a shorter elapsed time, thereby achieving more indepth understanding of the physical system operation and better, more reliable designs. Since solutions of complete dynamic models would take an
inordinate amount of time on digital computets,
simplifying assumptions are often made which can
lead to erroneous results. With the modern hybrid
computer, there is seldom any difficulty in obtaining
accurate, repeatable results for sophisticated
dynamic models.
COMPUTER
The low cost of studies employing hybrid computers, which has been documented many times in
published literature,2'3 is further enhanced in thirdgeneration systems by the availability of extensive
software for program preparation, analog processor
setup and checkout, and real-time operating systems
for better on-line utilization. Typical industrial
hybrid computing centers are running at least a
two-shift operation with a multiplicity of jobs. Of
course, the low cost per run is a function of the
fact that the average hybrid system is about 10
times faster than a large digital computer, and its
cost is about 10 times less.
As previously described, successful scientific
analysis and design often involve interfacing
physical hardware or processes to the mathematical
model. The hybrid computer, which is inherently
a real-time device, can be easily initerfaced to any
type of analog or digital sensor or controller. The
high-speed processing facility of the hybrid computer
is sufficient for all physical systems, and its low
cost makes it economical to dedicate the hybrid
system while experimental runs are performed. The
digital CPU in the hybrid system can monitor
and document the results in any graphical or
printed form.
A natural outgrowth of the high-speed, low-cost,
and real-time nature of the hybrid systems is its
use for conversational analysis. This has always
been a valuable asset of analog computers, and the
modern hybrid system greatly augments this
facility. Extensive conversational software, alphanumeric/graphic displays, and high-speed, allelectronic setup provide for efficient conversation
between the user and the mathematical model.
These facilities minimize the chance of errors
and produce completely documented results in
engineering units. Also, wasted on-line time is
minimized since the user simply enters parameter
changes and the digital processor will set up and run
the program. In third-generation systems, the CPU
can be multiprogrammed to handle a second job
stream while the hybrid computer is used in a
conversational mode.
Third-generation hybrid computing systems
The structure of the third-generation hybrid computing system is shown in Figure 2. All system
input/output and control are performed by the
digital CPU. Up to six analog processors may be
used with a single digital CPU to provide a range
from 25 mathematic/logic computing blocks to about
1500 parallel blocks. In addition, an external digital
computer can be interfaced to the hybrid system
to provide both digital/digital transfer as well as
direct control of the analog processors. The digital/
digital communication may be performed locally
on dedicated, high-speed parallel buses or remotely
through telephone modems.
The primary operating terminal for the system in
Figure 2 is the hybrid graphics terminal-an
July 1976
enhanced Tektronix 4010. To provide direct display
of the continuous, scaled data created by the
analog processors, an analog port is added to the
4010. This port, which can be activated or deactivated by the CPU, is interfaced to the parallel
processors for the X, Y drive of the storage CRT
as well as logic signal control of blanking and
erasing. With this terminal the hybrid user can
create completely documented, continuous graphics
results for either conversational analysis or hardcopy. Vector-generated graphical plots of di'gital
data can also be superimposed on the analog
solutions. Of course, standard analog strip-chart
time recorders and dynamic CRT's can also be
added to the system.
In addition to the dedicated hybrid graphics
terminal, additional remote terminals can be interfaced to the digital processor through modems
from telephone lines. These remote terminals may
be operated exclusively as digital terminals, or,
by adding linear modems and the analog port,
the remote user can have a true hybrid graphics
display.
A range of mass memory units can be added
including disks and various speed/capacity magnetic
tapes which interface through a direct memory
access channel. These units provide storage for the
operating system, user files, and data files. The
universal controller also provides for expansion with
a variety of card readers, line printers, digital
plotters, and high-speed paper tape.
Hybrid programs are synchronized primarily by
the real-time clock. This unit is a register counter
which operates from a crystal pulse source. The
timing interval can be preset from the CPU and the
count can be monitored on the I/O bus. Also, the
real-time clock is interfaced to the parallel processors so that it may be triggered from parallel
logic programs and the interval pulse can be used
to control analog program operation.
In addition to the primary operating terminal,
multiple hybrid terminals can be added to the universal controller to provide multiuser operation.
This is particularly useful in an educational environment where a group of students may access the computer simultaneously.
A modern analog processor consists of hardware
components, each of which is capable of performing
certain fixed mathematical operations:
*
*
*
*
*
*
*
*
*
*
integration,
summation,
multiplication,
arbitrary function generation of the form y = f(x),
certain fixed functions such as y = sin (x), y = log(x),
compare,
switches,
simple logic operations (AND, OR, NOT),
single-bit memories,
counters, shift registers.
The variables of the problem to be solved are
represented by signals in the analog processor, and
17
EXTERNAL
ANALOG
DEVICES
Figure 2. Hybrid system structure
each component can operate on these signals as
dictated by the mathematical equations describing
the problem. The computer is programmed by patching together, with actual patching wires, the collection of operations necessary to solve the equations
of the problem. Some of the characteristics of the
analog computer are:
* accuracy 1 part in 104;
* fixed point operations, dynamic range of ± 1;
* parallel operation (solution evolved continuously
in time);
* limited memory;
* limited arithmetic capability for complicated
algebra;
* changes made easily and directly;
* all results available at all times.
Because of the continuous and parallel nature of
the analog components, the interface with the
designer is intimate; by using the variety of display
devices available, he is able to investigate in detail
any portion of the system being studied at any
time during the solution. Changes to the patching
or component characteristics can be made easily
during the solution, and the effects of these
changes can be immediately seen. Since the com18
ponents operate in fixed point, there is a one-to-one
correspondence between the analog voltages being
manipulated and the signals of the problem being
studied. Interpretation of results is direct, on-line
during problem solution. As an example of the use
of the analog processor, consider a simple one-body
system which is described by Newton's law:4
mx=
Fi
where m is the mass of body, x the acceleration
of the body, and the sum or forces acting on the
body is
i
Fi = Fx + FD +FS= FX KDX
KsX
where Fx is some external force, FD the damping
force, KD the damping coefficient, Fs the spring
force, Ks the spring coefficient, and
FD
=
-KDX,
Fs
=
KSx.
COMPUTER
Since the analog computer is a fixed point device,
amplitude scaling must be introduced so that scaled
variables can be operated upon by the analog
components. The mathematical model representing
the one-body system would be written as
FmM
IM
Fx
MY
mx/
( KDXM)
M\ mx/
L
XM ]
LxMJ
where the subscript M is used to denote the maximum value of a variable. This would be solved
by the analog circuit of Figure 3.
(_FM\
mxMj
Figure 3. Analog solution of example
The analog processors are usually set up and controlled from the digital CPU through its I/O bus,
although those tasks may also be performed by the
external digital computer. Electronic coefficient devices can be set in a few microseconds each, and
function generators can be loaded in hundreds of
microseconds. This means that, after insertion of
the interconnection panel, the entire analog processor can be set up in a few milliseconds. New,
all-electronic digital voltmeters permit selection and
readout of mathematic/logic blocks at over 200 per
second. Complete setup and verification can be
performed in about 10 seconds. Analog-to-digital
and digital-to-analog data transfer can be accomplished
on both the I/O bus and DMA simultaneously.
A/D conversion of multiple channels can be typically
performed at up to 125,000 15-bit words per second
and digital-to-analog conversion can proceed at up
to 300,000 15-bit words per second. All digital-toanalog converters provide the product of an analog
variable by a digital word. Data transfer through
the DMA may include "wraparound" addressing so
that a large buffer containing many samples of a
number of analog functions can input or output
synchronously at up to maximum data rates using
a single CPU instruction.
July 1976
Hybrid operating systems
The users of hybrid computation range from
biomedical specialists with little or no knowledge of
computer technology to electrical engineers with a
comprehensive understanding of analog and digital
computers. Potential applications cover the full
spectrum of scientific analysis from theoretical
mathematical studies to on-line, real-time data
reduction and control for experimental laboratories.
Therefore, on the one hand the operating system
for hybrids must provide the convenience of Fortran
batch processing, and on the other hand the user
demands maximum run-time efficiency for highspeed, real-time operation. The system should also
provide convenient, powerful interactive facilities
for effective conversational use, not only for the
digital processor but equally for the parallel analog
processor and interprocessor communication.
To satisfy this unique diversity of requirements,
the operating system is composed of a hierarchy
of language processors and executive systems. The
structure of language processors is shown in Figure 4.
This hierarchy, which has evolved over a 10-year
period, permits the programmer to trade speed and
convenience as necessary to handle each application
efficiently. The interpretive processor is most convenient to use since it incorporates the entire system, including the parallel analog processor, into
a common syntax. Any digital program or portion of
a hybrid program in which speed of execution is not
MAXIMUM
CONVENIENCE
HOI
CONVERSATIONAL
INTERPRETIVE
PROCESSOR
t
t
COMMON
DATA
CONTROL
LINK
MATH
LIBRARY
STANDARD
FORTRAN IV
ANALOG/
SCALED FRACTION
DATA TYPE
IN-LINE
ASSEMBLY
DIGITAL
INTERFACE
LIBRARY
SCIENTIFIC
APPLICATION
LIBRARY
COMMON
SUBROUTINE
DATA
LINK
ASSEMBLER
MAXIMUM
SPEED
Figure 4. Hybrid programming language hierarchy
19
a major factor can be prepared most easily in the
interpretive language. Typical applications are for
complete, automatic setup and verification of the
parallel analog processor, conversational control of
complete hybrid program execution, and computation of complex algebraic expressions during the programming process and for on-line program changes.
To ensure a compatible hierarchy of programming,
facilities are provided to communicate data with a
compiled Fortran program. Also, control can be
transferred from the interpretive processor to a precompiled Fortran subroutine. When the subroutine
returns, the interpretive processor continues at the
next step.
The main digital run-time program may be prepared in Fortran using floating-point (REAL) data,
and complete mathematics libraries for all ASA
standard Fortran data types are provided. In addition, a library of subroutines is provided to convert
REAL/fixed-point data for communication with the
analog processors, An extensive scientific applications library for numerical integration and statistical
analysis is also typically provided.
When applications demand greater speed than can
be obtained using floating-point arithmetic, the programmer can use single 16-bit memory cells to
represent scientific data scaled in the range ±1,
which is the same range as data scaled on the
analog processors or obtained from experimental
laboratories through the A/D converter. All Fortran
operations permitted with REAL data can be performed with the scaled form with a significant
increase in speed and reduction in core used.
If a further increase in speed or savings in core
is required, the programmer can insert assembly
code in-line with Fortran statements. Also, in-line
assembly code may be used to access hardware
features that may not be directly accessible in
Fortran or through the libraries. Finally, if a large
amount of assembly code is required for extremely
time-critical loops, the programmer can prepare Fortran-compatible subroutines called by the main
Fortran program.
gain, etc. These developments have made it practical
to implement and use compiler languages to generate
programs automatically for the analog processors.
With EAI systems, for example, an analog program compiler called ECSSL is available. The source
language is Fortran based with extensions to specify
differential equations and certain unique parameters
needed to produce scaled analog programs. As
indicated in Figure 5, the system analyst starts
with a statement of the problem composed of a set
of algebraic and/or differential equations, a set of
constants and design parameters, specification of
arbitrary functions, and initial conditions for differential variables. Also, an estimate of maximum
values of state variables is needed for the program
scaling. The user translates this problem statement
into a Fortran-based syntax and punches cards to
provide the source language for ECSSL.
The ECSSL compiler is itself written in Fortran
and must be executed on at least a mediumsize digital machine such as an IBM 360/40 or
an SEL 32/50. A file specifying the configuration
of available computing blocks on the Pacer analog
processor can be maintained in the system or
entered on a deck of cards. The ECSSL compiler
first reduces the equations into individual operations
to be performed by the mathematic/logic blocks.
It then orders these operations for digital computation and scales all variables to a range of ±1.
ECSSL imposes a set of static operating conditions on the program for checkout purposes when
the parallel program is set up. If a portion of the
program includes differential equations, the digital
computer can carry out a solution of the problem
for dynamic check purposes. Finally, the available components are assigned to each operation; and
the ECSSL compiler generates the listings shown in
Figure 4, as well as a magnetic tape file in the
Hytran interpreter source language, which provides all the information needed to patch, set up,
check out, and run the analog/hybrid program. (Hytran is the name used by Electronic Associates for its
on-line interpretive processor on standard hybrid
systems.)
Automatic program preparation for parallel
analog processors
Applications of hybrid computation
For most applications published in the literature
the efficiency in performing runs on the hybrid
computer has been well documented. However, the
programming effort was usually greater than preparing an equivalent all-digital computer program
in a simulation language or in Fortran. The bulk
of the additional effort is in preparing the. scaled
interconnection program for the parallel analog
processor, obtaining essential program verification
data, and documenting the analog program.
Modern analog processors are much easier to program than earlier analog computers due to the use
of "black box" computing elements. These elements,
such as digitally controlled attenuators and function
generators, eliminate the special considerations
of electrical characteristics such as loading, limited
20
The applications of hybrid computers are as varied
as are the uses of modern scientific technology.
Third-generation systems further advance the range
of applications by providing higher speed/accuracy,
new components which introduce new computing
techniques, sophisticated graphic displays, and
reduced programming effort and cost. Rather than
attempt to summarize all the applications of hybrid
computation, certain specific examples are outlined
that demonstrate unique benefits of the latest
hybrid systems.
Some of the major fields in which hybrid computation is being used are listed in Table 1. In most
organizations both large digital computers and
hybrid systems are available, and rational decisions
are made to carry out studies using either or
COMPUTER
r
IBM
360/40
--.
_
SPEC~~~IAL
|
{
|
|
t ~~~COMPONENT
-I
_
')
CLER
COMPONENT
CONNECTIONS
I
'-
I
-
u~ ~ I
]Rocket engine controller for the Space Shuttle.
As a part of the task of designing the throttleable
rocket engines to be used in the Space Shuttle,
Honeywell must simulate the rocket engine being
developed by Rocketdyne and, using both a mathematical model of the controller and actual controller prototypes, must develop and evaluate the
algorithms and parameters of the controller. A
Fortran digital model of the system was developed
which runs on a CDC 6600 at 50 times slower than
both of the systems, depending on the needs of the
study. In industry and government installations,
nearly all complete integrated hybrid systems are
utilized more than one shift per day and, in some
installations, more than two shifts. The use in
educational installations varies, but where complete
systems are available, utilization is generally high.
The following paragraphs outline a few specific
studies that indicate the unique capabilities of
modern hybrid systems.
STATIC
CHECK
_
-
IBMIN
PACER 600
_
I
_
J~~~~~~~~~~~~~~~~~~~
It
I
STANDARD
IAN
_
INTER RETER . K
TT
_
I
I_
I
SOUIOI
FI
_ .
EAI
TE
I
{STANDARD
SETUP
iEXECUTIVE
\==
I
SPECIAL
SETUP
rlvfr^l ._Vetfr
PATCHING
CONNECTIONS
I
I
o. *
~~~~~~~STATIC
\~~ TEST
HY
I
I
I
|IRUN.TIME
L_ _I
_
__
I~~~~~~~~~~~~~FLE
_
I
I
Figure 5. The EAI ECSSLI360 processing system
July 1976
21
real-time. Also, the model has been run on an
XDS Sigma 5 at 160 times slower than real time.
These models are limited for design purposes and
cannot be used at all for real-time operation with
the prototype controllers.
Honeywell also had a large first-generation hybrid
system composed of six EAI-231R computers and a
Table 1. Major fields of hybrid computer application
INDUSTRY
MISSILES/SPACE VEHICLES
AIRCRAFT/HELICOPTERS
AVIONICS/RADAR SYSTEMS
TURBINE ENGINES
AUTOMOTIVE/OFF-HIGHWAY VEHICLES
MARINE VEHICLES
GASOLINE/DIESEL ENGINES
CHEMICAL PROCESS
PETROLEUM REFINING
METALS PROCESSING
UTILITIES/ELECTRICAL DISTRIBUTION
NUCLEAR POWER PLANT DESIGN/SAFETY
ELECTRONICS
GOVERNMENT
NASA-SPACE SYSTEMS
WEAPONS DEVELOPMENT/MISSILES
VEHICLE RESEARCH/TESTING
ENVIRONMENTAL PROTECTION AGENCY
DOT-SAFETY/HIGH SPEED TRANSPORT
BIOMEDICAL RESEARCH
WATER RESOURCES/POLLUTION
EDUCATION
UNDERGRADUATE EDUCATION
GRADUATE RESEARCH
SPONSORED RESEARCH
REAL-TIME
CONTROLLER
MODEL
Sigma 5. On this system, the model also ran at
only 50 times slower than real time since the problem
frequencies are up to 250 Hz. Following an evaluation, it was decided that an EAI 700 system with
two 781 analog/hybrid processors could simulate
the rocket engine in real time. This system, as outlined in Figure 6, was subsequently purchased and
installed at Honeywell with an interface to a Sigma
5 which will be used to model the controller.
When the prototype controller is developed, it will
replace the -Sigma 5 model for final design and
evaluation.
If one assumes that a CDC 6600 is capable of
one million instructions per second, the Pacer 700
will be running at the equivalent of 50 MIPS
an estimate which checks well with the author's
data.
Nuclear plant simulation. This application involved the simulation of the Pickering Nuclear
Generating Station control to supplement the design
work of individual loops and to review the performance of the plant control system before the
plant went up to power.5 Graham Crate Associates
carried out the study for Atomic Energy of Canada
Ltd. using the EAI 690 (predecessor to Pacer 600)
at the National Research Council in Ottawa,
Canada. The mathematical model for the nuclear
power plant was distributed between the 640
digital computer and the 680 analog computer as a
function of speed and data storage requirements.
Scaled fraction arithmetic in Fortran was used
exclusively, giving a 10/1 speedup over what could
have been obtained using real arithmetic. Included
in the mathematical model were 40 first-order
differential equations, 55 algebraic equations, 13
nonlinear functions, 9 time delays, 6 sampled
variables, 12 limited variables, and 6 condition
switches.
This entire study was performed on the 690
hybrid system with one 680. The simulation verified the basic design of the control system, and
several improvements in the control laws were
found to improve the dyanmic behavior of the plant.
XDS SIGMA 5
EAI PACER 700
2 X 781 ANALOG
PROCESSORS
100 DIGITAL
PROCESSOR
ENGINE
DYNAMICS
FUNCTION
GENERATION
Figure 6. Real-time shuttle enginelcontroller model
22
COM PUTER
Power train-vehicle modeling. One industry in
which the use of hybrid computation is growing
rapidly is land vehicles, including automobiles,
trucks, and off-highway vehicles such as earth
movers, road scrapers, tractors, etc. An example
of an application was the simulation of a power
train-vehicle svstem by Caterpillar Tractor Company.6 The transmission model, which was for a
two-axle, rubber-tired tractor-scraper hauling vehicle,
was designed to represent accurately shifting
transients for seven levels of clutch-actuated "gear"
changes. Some of the objectives of the study were
to optimize the system design parameters and to
evaluate power train component capability and
vehicle shift-feel.
The study was originally implemented on two
EAI 680 analog computers with a simple data
interface to a CDC 3300 at the Caterpillar
Research facility in Peoria, Illinois. It took about
two days to manually set up and check out the
program since the analog implementation required
a large number of switched coefficients for the
various clutches. However, very good correlation
with actual vehicle data was obtained from the
simulation. The results of the study included (1) indepth understanding of the power train-vehicle
dynamics; (2) improved transmission design parameters to improve shift-feel and clutch life; and
(3) predicted life for gears, bearings, and drive
shafts according to cumulative fatigue damage
theory.
The use of a Pacer 600 hybrid system was also
evaluated for this study.7 It was found that by
use of electronic DCA's in place of the earlier
servo-set potentiometers on the analog processor
and with digital analysis of clutch lock, it was
possible to implement the same model using a
single 681 with very few parallel-logic driven
switches. The speed of solution would be the same,
,<iv
PLENUM
but with the Pacer 100 controlling the runs, more
fully documented results are obtained in less overall
time. Also, instead of a two-day setup and checkout
on the all-analog model, the Pacer 600 hybrid program can be loaded and verified in less than 10
minutes. In addition, the dedicated digital processor can handle the task of data reduction to
determine cumulative tdamage which was previously
delegated to the CDC 3300.
Single-blow heat exchanger. A common problem
in the design of a wide variety of mechanical
chemical systems is the choice of a surface for heat
exchangers that will transmit maximum heat with
the least pressure drop in the hot gas. As part
of the solution of the design problem, it is necessary
to test surfaces to determine the heat transfer
coefficient. A sketch of the mechanism used to perform a single-blow heat transfer test is shown in
Figure 7. Initially, the control surface allows ambient temperature gas (air) to pass through the
test surface until the output temperatures Tg and
TS have reached ambient and the test is in steady
state. Then the control surface rapidly switches to
introduce the hot gas source, and the outlet temperature transients are monitored until a steady
state is again reached.
These transient curves are a measure of the heat
transfer characteristics of the surface, but to obtain the actual heat transfer coefficient, it is necessary
to model the test mathematically. The partial
differential equations (PDE's) which govern this
process are
aT
Tg -Ts+
as2
S NXaT
ax
N (TS
Tg)
SOLID TEMPERATURE
(TSQ)
GAS TEMPERATURE
(TGV)
GAS FLOW
Figure 7. Single-blow heat transfer test
July 1976
23
where X is the longitudinal heat conduction coefficient, and N is the heat transfer coefficient. The
parameter X can be accurately determined for the
material separately from the single-blow heat transfer test. To determine N from the test, an initial
guess is made and the model is solved. The resulting
output temperatures are, compared to the test
results, an error is computed, and N is changed in
a direction to. minimize the error. After a sequence
of iterative runs, a minimum error is obtained and
the resulting N is the desired value of heat
transfer coefficient for that test condition.
This prpblem is presently solved on a large GE
615 digital computer which requires 2 seconds of
CPU time for each run of the PDE's. Since a
number of tests are performed for each material
and many surfaces must be tried before the desired
characteristics are obtained for each purpose, this
represents a major computing load.
The problem was programmed on a Pacer 600
system using the ECSSL analog compiler for a
parallel representation of the PDE's using finite
differencing in x. The 681 program was obtained
from ECSSL, set up on the analog processor, and
checked against the ECSSL dynamic check in 2
days of elapsed time. A hybrid graphics program
was prepared in Fortran for display of results and
interfaced to EAI's Hytran interpreter for executive control. In addition, a simple program was
written in Hytran to accept a test function and
iteratively solve the model to determine the heat
transfer coefficient.
The parallel solution of the equations ran in 0.2
second on the Pacer 600 and complete, graphically
documented results were obtained as shown in
Figure 8. Also, telephone modems were set up to
operate this program remotely from West Long
Branch, New Jersey, to Detroit.
Conclusions
Modern hybrid computation is a practical, viable
technology for a wide range of applications.
Although electronic data processing equipment has
become faster and somewhat less expensive in recent
years, it is still far behind the speed and economy
offered by the latest generation of hybrid computer
systems. Programming large digital computers for
scientific applications such as continuous system
simulation has become easier by the introduction
of special programming languages; however, the
basic speed and interactive limitations still exist.
The latest improvements in hybrid computing
systems reduce programming/setup time and effort,
allow larger problems to be solved on smaller, less
expensive systems, and significantly enhance system
productivity. Hybrid computers are no longer experimental machines programmed by a few specialists
for one or two applications. They are a proven
tool for day-to-day use by the average engineer
or scientist who needs to find the best solution
for a problem. U
;S J. Paul Landauer is
a staff engineer in the
5 Scientific Computation, Marketing Department of Electronic Associates, Inc. where he
is presently responsible for the design of new
hybrid computer system capabilities to meet
application requirements. His interests span
all computer disciplines as applied to con-
tinuous system simulation including analog,
digital, and hybrid hardware, software, and
ionwro applications. In particular, he has recently
been involved in developing new compilers to facilitate preparation and setup of hybrid computer programs.
Landauer holds a BSEE from New Jersey Institute of
Technology and has done graduate work at the University
of Pennsylvania.
References
RUNI
N s
LAM8
SINCLE-BLOWd HEAT EXCAGER
2 000
1. eeeO
I a
RUN2_
N_3
LAMB_ 0
J. P. Landauer, "Quantitative Comparison of Analog and
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2.
B. A. Chubb, "Economic Evaluation of the CSMP
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9
8
RUN13_
N_ 18
LAIB_ e
7
RUM-
9_ 1l
LAMB_ .5
1.
6
TG.
4
3
5.
2
-l1
.e
2.0
4.8
TIME
6.0
8.0
Figure 8. Graphic display of solutions for single-blow heat
exchange model
24
is's6
6.
L. G. Koch, "Power Train-Vehicle Modeling to Simulate
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COMPUTER