Hybrid Simulator for Compressible Fluid Flow

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 V a r n a – B u l g a r I a

2. CONTENTS • Introduction • Description of the Hybrid Simulator • Conservation of Mass, Energy and Momentum • Analog Relations • Time Constants • Experimental Results • References • Literature

3. INTRODUCTION COMPUTERS ANALOG COMPUTER DIGITAL COMPUTER QUANTUM COMPUTER HYBRID COMPUTER SIMULATORS EQUATION SOLVERS HYBRID SIMULATOR

4. INTRODUCTION

5. 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.

6. 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.

7. 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.

8. INTRODUCTION • The electronic circuitry of the newly developed analog integrator in "reset" position

9. DESCRIPTION OF HYBRID SIMULATOR • The proposed hybrid simulator consists of four parts. • The three parts to the right side are available on the market. • 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 Display and Printout M F Main Frame Analog - Digital Hybrid Simulator (Compressible Fluid Flow Simulator) P C Digital Computer D A S Data Acquisition System

10. 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.

11. DESCRIPTION OF HYBRID SIMULATOR • Smallest possible working unit of the compressible fluid flow simulator.

12. DESCRIPTION OF HYBRID SIMULATOR

13. CONSERVATION OF MASS, ENERGY AND MOMENTUM • The three equations considered and integrated under "run" conditions are mass, energy and momentum. * *) = Heat generation as a result of viscous friction.

14. 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

15. 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

16. 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: The double index subscripts mean "from the first-index integrator outlet to the second-indexintegrator inlet" where the indices d, e, m and νrefer to "density", "energy", "momentum" and "viscosity", respectively.

17. 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 and the difference and feeding it to the internal energy capacitors, while the bulk 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.

18. 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)

19. 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").