Transcript Slide 1

Hybrid Simulator for
Compressible Fluid Flow
Prof. Dr. Nuri Saryal
Middle East Technical University
Ankara - Turkey
International Conference
Advances in Physics and Astrophysics
Of the 21. Century
September 6 - 11, 2005
Varna–BulgarIa
Hybrid Simulator for Compressible Fluid Flow
CONTENTS
Introduction
Description of the Hybrid Simulator
Conservation of Mass, Energy and Momentum
Analog Relations
Time Constants
Experimental Results
References
Literature
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
COMPUTERS
ANALOG
COMPUTER
DIGITAL
COMPUTER
QUANTUM
COMPUTER
HYBRID
COMPUTER
HYBRID
SIMULATOR
SIMULATORS
EQUATION
SOLVERS
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
Subject
Time continuous integration
Data processing, storage, display and printout
Large size parallel computing
Topological similarity
Mathematical operations
Convergence problem
Space discretion
Analog
Digital
Hybrid
Simulator Computer Simulator
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
•In the past, an analog simulator was constructed to analyse
compressible fluid flow [6].
•The one-dimensional model had four identical cells, each cell
representing one cubic meter volume of space.
Two were assumed to be located "above" the other two, to
introduce the effect of gravity.
Each cell had one (internal) energy and one mass (density)
integrator. The cells were interconnected through momentum
integrators.
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
•The model was not realistic but satisfied all the requirements of a
"chaotic" system:
Simulation of a sudden extraction of a fixed amount of heat energy
from one of the "lower" energy integrators, causing shock waves to
bounce back and forth, giving a different pattern each time, but the
total mass of the system was constant and the total internal energy
decreased by the amount extracted, otherwise it was constant.
High viscosity was simulated through the momentum integrators to
shorten the running time, because the integrators were stable for only
five to ten seconds and after each experiment the operational
amplifiers had to be readjusted. There were some more deficiencies,
not of interest anymore.
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
•After years of hard work, the above-mentioned deficiencies were
eliminated and a simple, low cost and extremely accurate (open ended,
max. 1% drift per hour) analog integrator was developed.
•The new system is an analog-digital hybrid, consisting of a great number
of cells, each containing (as before), one energy, one mass and for each
dimension one momentum integrator, providing energy, mass and
momentum transfers between neighboring cells time continuously.
•Integration, summing and multiplication of variables by a constant are
performed time continuously in the analog part.
•In the past, multiplication and division of variables (time dependent
voltages) were performed through analog circuitry time continuously, but
will be done digitally by programmable micro controllers (one in each
cell), in the future.
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Hybrid Simulator for Compressible Fluid Flow
INTRODUCTION
The electronic circuitry of the newly developed analog integrator in "reset" position
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Hybrid Simulator for Compressible Fluid Flow
DESCRIPTION OF HYBRID SIMULATOR
The proposed hybrid simulator consists of four parts.
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The three parts to the right side are available on the market.
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The "Main Frame" contains a great number of cells, each
representing a particular control volume in the flow field,
consistent with the topology of the flow field.
•
A two dimensional frame would resemble a chessboard with
its positive (assume black) and negative (assume white) cells. A
pair of adjacent black and white cells making up the smallest
possible working unit, are interconnected in the “run” position.
General layout of the proposed analog simulator
MF
Main Frame
Analog - Digital
Hybrid Simulator
(Compressible Fluid
Flow Simulator)
DAS
Data
Acquisition
System
PC
Display
Digital
and
Computer
Printout
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Hybrid Simulator for Compressible Fluid Flow
DESCRIPTION OF HYBRID SIMULATOR
Analog integrator is the "heart" of the simulator. It consists of
 one capacitor C(t),
 two (or more) "input" resistances (to the right of nodes [N1 A]
and [N1 D]
 and the operational amplifier [A1] (lower left).
The rest of the circuitry keeps the left leg of the capacitor
under "run" conditions at "zero" potential (virtual earth) with high
accuracy and output of the integrator, (the right leg of the capacitor
C(t)), is available with ±10 μV accuracy on the output node [N2].
Any current flowing in or out through nodes [N1] will be integrated
by [A1] over C(t) and the result will appear at the node [N2]
uninterrupted, time continuously.
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Hybrid Simulator for Compressible Fluid Flow
DESCRIPTION OF HYBRID SIMULATOR
Smallest possible
working unit of the
compressible
fluid
flow simulator.
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Hybrid Simulator for Compressible Fluid Flow
DESCRIPTION OF HYBRID SIMULATOR
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Hybrid Simulator for Compressible Fluid Flow
CONSERVATION OF MASS, ENERGY AND
MOMENTUM
The three equations considered and integrated under "run"
conditions are mass, energy and momentum.
 
 
d
V
   (  v )  n dS   (  v )  S
S
dt
d (cv T )
 
 
V
  c p  (  T v )  n dS   c p  (  T v )  S   *
S
dt



  


V  v    (  v ) v S  V b   p S   S
S
t
*)

= Heat generation as a result of viscous friction.
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Hybrid Simulator for Compressible Fluid Flow
ANALOG RELATIONS
The electrical analogy between the mechanical fluid system and its electrical
analog model:
Standart conditions:
T0 = 290 K
p0 = 1 bar
0 = 1.2 kg/m3
udo = 7 V
U0 = 250 kJ/kg (internal energy)
ue0 = 5 V in the electrical circuit.
The ratio udo/ueo = 7/5 was selected on purpose to be equal to the ratio
of specific heats cp/cv = 1.4
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Hybrid Simulator for Compressible Fluid Flow
ANALOG RELATIONS
The system (actual)-to-model (circuit) ratios of analogy utilized are as follows:
Mass (density) and energy (internal) are scalars and represented by
volatages ud and ue on the integrator capacitors, respectively
The other system to model analog ratios are as follows:
n0 = Δt/ Δtel [s/sel]
n1 = m /Q [kg/C]
n2 = V/C [m3/F]
n3 = ρ/ud [kg/m3V]
n4 = S∙R [m2Ω]
n5 = cv∙ ρ∙T/ue [J/m3V]
n6 = ρ∙v/um [kg/m2sV] [Ns/m3V]
where
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Hybrid Simulator for Compressible Fluid Flow
TIME CONSTANTS
All connections between integrators have an electrical resistor.
The size of the resistor can be calculated from the Time Constant “ "
relations given below:
 em 
Vcv
S  n0  E
 dm
 md 
Vcv  E

S  n0  g  hL
Vcv
S  no  E
 vme
 me 
Vcv
S  n0  k  E
Vcv y

2 S    n0
The double index subscripts mean "from the first-index integrator outlet to the
second-index integrator inlet" where the indices d, e, m and ν refer to "density",
"energy", "momentum" and "viscosity", respectively.
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Hybrid Simulator for Compressible Fluid Flow
EXPERIMENTAL RESULTS
So far, two cells, has been constructed and tested without the micro
controller, using DAS-20, donated by A.v.Humboldt Foundation.

The micro controller has the function of calculating both H and the
difference H  H  H 0 and feeding it to the internal energy capacitors,

while the bulk H 0 is transferred directly (Enthalpy correction).
The analog integrators have an openended drift of less then 1 % in
one hour. The "white" and "black" cell arrangement renders stability and
simplicity to the model.
That the principles of mass, energy and momentum conservation are
satisfied by the proposed hybrid simulator were proven experimentally
in [6].
The main difference is, that the multiplication and division of votages,
representing time dependent functions were performed by analog
circuitry, now it will be done by digital micro controllers.
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Hybrid Simulator for Compressible Fluid Flow
REFERENCES
1) Saryal, N. "Lösung des Temperaturverteilungsproblems in Rotoren
von Dampfturbinen beim Anfahren, im satationaeren Zustand und beim
Abschalten durch die elektrische Analogie-Methode" (Ph.D. Thesis,
Berlin 1956)
2) Saryal, N. "Solution of Transient State Thermal Stress Problems
Through Electrical Analogy." (METU 1966, Engr. Faculty Publication No.
16)
3) Saryal, N. "Electro-Analog Models for Heat Exchangers and
Simplified Method for Heat Exchanger Calculations." (Int. J. Heat Mass
Transfer, Vol.17 pp 971 - 980 Pergamon Press 1974)
4) Saryal, N. "Beuken Model for Complicated Diffusion Systems",
(Elektrowaerme International, Vol.39 pp., August 1981)
5) Saryal, N. "Elektrische Analogie von Druckwasser-Kernreaktoren."
(Waerme, Vol.87 Nr.1 pp 5 - 9 , Febr. 1981)
6) Sönmez M. “A New Double Hybrid Computer System to Analyse
Natural Convection Heat Transfer” (Dissertation, METU, Ankara, 1995)
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Hybrid Simulator for Compressible Fluid Flow
LITERATURE
1) Sterling T. "How to Build a Hyper Computer" (Scientific American,
July 2001, pp. 28-35 especially; tabulated information on pages 31
and 32).
2) Hoffman R. N. "Controlling Hurricanes" (October 2004, pp. 38-45,
esp. page 41 "Modeling Chaos").
3) Lloyd S. and NG Y.J. "Black Hole Computers" (November 2004, pp.
30-39, esp. page 34, first and second column).
4) Glatzmaier G. A. and Olson P. "Probing the Geodynamo" (April
2005, pp.32-39, esp. page 37 "What Might Be Missing").
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