An “ideal equivalent gas method” for the study of shock waves in supersonic real gas flows

Summary A method developed by the author for the systematic study of the thermodynamic and dynamic properties of the gas behind a shock wave is reported.The method is applicable to supersonic flow regimes for which the excitation, dissociation and ionization effects invalidate the usually adopted hypothesis of ideal gas.An Ideal Equivalent Gas, having the ratio of the specific heats _s dependent on Mach number and altitude of flight is postulated.On the basis of the mass, momentum and energy conservation equations, valid through the shock wave, the relations defining the thermodynamic and dynamic state of the gas behind the shock wave are derived. These relations establish an extension of the classic relations valid for the ideal gas and reduce to them identically for _s=.The dependence of the ratio of specific heats _s of the Ideal Equivalent Gas on Mach number and altitude has been established, over a wide range, on the basis of the real gas solutions derived by Huber.

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Sommario Nella presente nota viene esposto un metodo sviluppato dall'autore per lo studio sistematico dello stato termodinamico e dinamico del gas a valle di un'onda d'urto in regime supersonico, allorchè cioè gli effetti dell'eccitazione dei gradi di libertà vibrazionali delle molecole e della loro dissociazione e successiva ionizzazione invalidano l'ipotesi di gas ideale generalmente adottata.Viene definito un gas ideale equivalente avente rapporto dei calori specifici _s funzione del numero di Mach e della quota di volo ed in base alle equazioni di conservazione della massa, della quantità di moto e dell'energia, valide attraverso all'onda d'urto, vengono derivate delle relazioni definenti lo stato termodinamico e dinamico del gas a valle dell'onda d'urto. Tali relazioni costituiscono una estensione delle classiche relazioni dell'urto valide per il gas ideale alle quali si riducono per _s=.La dipendenza del rapporto dei calori specifici _s del gas ideale equivalente, dal numero di Mach e dalla quota è stata stabilita sulla base delle soluzioni ottenute da Huber per il gas reale.

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On linear versus nonlinear flow rules in strain localization analysis

Summary This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear comparison material is critically reviewed and compared to the criterion resulting from actual nonlinear plastic flow laws.

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Sommario Si svolgono alcune considerazioni sui fenomeni di biforcazione in solidi elastoplastici in regime di piccole deformazioni (di linearità geometrica) e precisamente sul manifestarsi di localizzazioni intese come discontinuità nel campo delle deformazioni incrementali. Si considerano leggi nonassociate. Vengono così inclusi nella trattazione modelli costitutivi frequentemente adottati per descrivere il comportamento di materiali ad attrito interno e soggetti a danneggiamento (nel senso di degrado di rigidezze elastiche in seguito a deformazioni anelastiche), oltre che soggetti a manifestazioni di instabilità per incrudimento negativo (softening). Si esamina criticamente il criterio, frequentemente adottato in letteratura, di localizzazione fondato su materiale di confronto incrementalmente lineare e si fornisce, corredato da osservazioni comparative, il criterio che risulta dall'assunzione del modello di materiale incrementale non lineare

     

First order phase equilibrium for classical bodies

Summary In this note the Author gives a general and unified treatment of first order phase equilibria for classical bodies like those considered by Truesdell and Toupin in[3].The Author reaches a system of partial differential equations (generalized Clapeyron equations) the conditions of whose solution are shown always to be satisfied.In particular, the Author derives the equations governing the polarized phase equilibrium for a fluid.Besides the equations ruling the phase equilibrium for a two phase n-component fluid mixture are given and the equivalence with the statical Gibbs-Duhem relation is shown.

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Sommario In questa nota l'Autore presenta una trattazione generale ed unificata degli equilibri di fase del primo ordine per corpi classici come quelli definiti da Truesdell e Toupin in[3].L'Autore perviene ad un sistema di equazioni alle derivate parziali (equazioni di Clapeyron generalizzate) del quale si dimostra la integrabilità.In particolare, si deducono le equazioni che governano gli equilibri di fase polarizzati.Inoltre si ottengono le equazioni che regolano l'equilibrio di fase per una miscela fluida a n componenti; in questo caso si dimostra l'equivalenza delle equazioni con la relazione statica di Gibbs-Duhem.

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This work was supported by the Gruppo Nazionale per la Fisica Matematica of C.N.R.     

Particle-in-a-box study of the evolution of an ion-acoustic shock wave

In an analysis of a one-dimensional numerical model of a nonisothermal plasma it is shown that an ion-acoustic shock wave of subcritical amplitude separates a soliton from the shock front after the reversing stage. This process is accompanied by turbulent flow behind the front and by trapping of ions in potential wells. The numerical particle-in-a-box method is being used widely to study plasma phenomena. One field in which this method has been found fruitful is in the study of a nonisothermal plasma, characterized by an ion-acoustic wave branch.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1971.The authors thank R. Z. Sagdeev for support and interest in this study.     

The effect of the sheet rigidity on strength of the spot weld tension shear joint

This paper presents some test and analysis results for a spot welded joint subjected to tensile and alternate load. The effect of sheet rigidity on the tensile strength and fatigue life of the spot welded joint is studied by using the stress intensity factorsK _I,K _II,K _III and an effective stress intensity factor K_max calculated by the finite element method for crack around the nugget. The results show that the effective stress intensity factor K_max is an essential parameter for estimating the fatigue life of the spot welded joint.     

Über die Übertragungseinheiten und ein „Vierfelderdiagramm” zur Berechnung von Wärmeübertragern

Zusammenfassung Es wird dargelegt, wie man nach Einführung des bekannten Begriffes Übertragungseinheit und mit Hilfe eines Vierfelderdiagramms zu einer relativ einfachen und durchsichtigen Berechnung von Gleich- und Gegenstrom-Wärmeübertragern gelangt.

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On transfer units and a four-quadrant-diagram for the calculation of heat exchangers

It is shown that the introduction of the known concept of a transfer unit and the use of a four-quadrant diagram leads to a relatively simple and clear computation method for co-current and counter-current heat exchangers.

     

Studies of Mental “Noise”

Successive tests of subjects' performance in reaction time tasks were treated as time series and submitted to spectrum analysis. Rather than revealing the white noise expected by the view that variability is due to random error (equivalent power across frequency), the power spectra revealed colored noise. The slopes of the power spectra did not vary much for tasks differing in memory requirements. Spectrum analysis of time series from the logistic map also showed colored noise in regions on the edge of chaos, showing that the presence of colored noise in cognitive data need not oblige a theoretical account based on a complex, high-dimensional, system.     

On elastic-plastic structures with associated stress-strain relations allowing for work softening

Summary For the elementary (finite or infinitesimal) constituents of the structure are assumed generalized stress-strain relations which satisfy the condition of normality but which may exhibit work-softening, concavity of yield surfaces, variation of elastic coefficients with stress and/or plastic strain.The usual phenomena of geometric instability are excluded. Sufficient conditions are formulated for overall stability in spite of the presence of unstable elements, and for uniqueness of the incremental boundary-values problem. Conditions are discussed with a view to applications and expressed in terms of positive definiteness of appropriate quadratic forms.Finally, yield surfaces and flow laws for the structure are examined, and among other things their necessary association is shown.

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Sommario Per i costituenti elementari (finiti o infinitesimi) della struttura si assumono legami incrementali tra sforzi e deformazioni generalizzati che soddisfano alla condizione di normalità ma che per il resto sono generici, cioè tali da presentare eventualmente incrudimento negativo, concavità del campo elastico, variazione dei coefficienti elastici con gli sforzi e/o con le deformazioni plastiche.Esclusi per il sistema i fenomeni usuali di instabilità geometrica si formulano condizioni sufficienti per la stabilità del complesso nonostante la presenza di parti a funzionamento instabile, e per l'unicità del problema incrementale al contorno. Le condizioni sono discusse in vista delle applicazioni ed espresse in termini di definizione positiva di forme quadratiche opportune.Si esaminano infine le superfici di snervamento e le leggi di scorrimento per l'intera struttura e, tra l'altro, se ne dimostra la necessaria associazione.

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First published in Italian in Rendiconti dell'Istituto Lombardo Classe Scienze e Lettere, A 100, 1966.The present investigation has been promoted and financed by the Consiglio Nazionale delle Ricerche (C.N.R.) at the Istituto di Scienza delle Costruzioni of the Facoltà di Architettura, Politecnico of Milano. Part of it was carried out at Brown University (Providence R. I. - U.S.A.). The author acknowledges with tanks the NATO Fellowship assigned by the C.N.R. in 1964, the encouragement and kind hospitality he received from Professor D.C. Drucker, and the interesting discussions he had with Professor Drucker and Dr. A. C. Palmer.     

Whose Thoughts Are They, Anyway? Dimensionally Exploding Bion's “Double-Headed Arrow” into Coadapting, Transitional Space

The physics and biology that found psychoanalysis account for discontinuous experience only in the presence of nonmeasurable, metaphysical operators; these include the ego and its subsystems as well as biological experience inherited through Lamarckian principles. Complex, self-organizing systems, however, can link biology to experience without metaphysics. They can also account for psychoanalytically relevant behaviors without appealing to stable internal representations. These behaviors include what W. R. Bion called transformation in O and its corollary, the appearance of the selected fact. By dimensionally exploding the double-headed arrow that he used to link the states Ps and D in his model for thinking (Ps D), we can generate a space that is, at once, psychoanalytically imaginal and dynamically coadapting. Isomorphic to D. W. Winnicott's transitional space, it is self-organizing. It is describable according to dynamics formulated by W J. Freeman, S. Kauffman and C. Langton and it can generate instantaneous conscious contents by way of a selective process analogous to spatio-temporal binding. As a whole, this model supports a clinical stance advanced by D. W. Winnicott as play, within transitional space.     

Some aspects of dilute suspension theory

A theory proposed by the author as representative of the flow of a general suspension contains three interaction forces, f, S and N. For a quasi-concentrated suspension and for a dilute suspension, N and S, N are omitted, respectively. For the latter special case, we treat diffusion of a fluid through an elastic solid. For a quasi-concentrated suspension, we show that F and S depend on the gradient of the motion gradient. We demonstrate the existence of interesting phenomena: non-simple behavior, dissipative effects, generalized lift and drag forces.Presented at the second conference Recent Developments in Structured Continua, May 23 – 25, 1990, in Sherbrooke, Québec, Canada.     

Application of the method of integral diffusion to investigation of turbulent transfer

A number of authors have critically examined semiempirical mixing length theories [1]. A defect of these theories is connected with the fact that the magnitude of the mixing length, which is assumed to be small in constructing the theory, turns out in experiments to be comparable with the characteristic dimensions of the flow region. Thus, the concept of volume convection [2–4] or integral diffusion [5], which is understood to be a transfer mechanism in which the friction stress is not expressed in terms of the velocity gradient, is introduced along with the concept of gradient diffusion. In addition, there are a number of experimental papers [6] in which it is shown that the turbulent friction stress cannot be equal to zero at the place in the flow where the derivative of the velocity is equal to zero. Mixing length theory does not describe this effect.It is possible to generalize mixing length theory [7–9] in a way which eliminates these defects. Flow of an incompressible fluid is considered.     

Group Classification of Equations of the Form y″ = f(x,y)

The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described.     

Line radiation in non local thermodynamic equilibrium

Summary This paper deals with the problem of line radiation in conditions of non thermodynamic equilibrium and applies the results obtained to the study of the imprisonment of resonance radiation. It was found that the excited level, and by consequence the resonance radiation, decays in two ways in competition each other: one is a diffusive decay, due to the fact that the gas is generally very thick for frequencies near the center of the absorption line, and the other is an exponential decay due to the far wings of the absorption coefficient, where the gas is optically thin.

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Sommario E' stata trattata la radiazione di linea in condizioni di non equilibrio termodinamico, e i risultati ottenuti sono stati applicati allo studio del cosiddetto intrappolamento della radiazione risonante. S'è trovato che il livello eccitato, e di conseguenza la radiazione risonante, decade in due modi in competizione fra loro: il primo è un decadimento di tipo diffusivo, ed è dovuto al fatto che il gas è generalmente otticamente opaco al centro della linea di assorbimento, mentre il secondo è di tipo esponenziale, ed è dovuto alle code del coefficiente di assorbimento, dove il gas è otticamente sottile.

     

Second order phase equilibrium for classical bodies

Summary In this note the Author, recalling a previous work[15], gives a new formulation of second order phase equilibria for classical bodies such as those defined by Truesdell and Toupin in[8].The Author arrives at three equivalent systems of partial differential equations (generalized Ehrenfest equations), the conditions for whose integration are shown to be always satisfied.Finally, as particular cases, the equations ruling the phase equilibria for classical fluids and for n component-classical fluid mixtures are given.

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Sommario In questa nota l'Autore, rifacendosi ad un lavoro precedente[15], presenta una nuova formulazione degli equilibri di fase del secondo ordine per corpi classici come quelli definiti da Truesdell e Toupin in[8].L'Autore perviene a tre sistemi equivalenti di equazioni alle derivate parziali (equazioni di Ehrenfest generalizzate) dei quali viene dimostrata la integrabilità.Infine, come casi particolari, si ottengono le equazioni che governano l'equilibrio di fase per fluidi classici e per miscele fluide classiche ad n componenti.

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This work was supported by the Gruppo Nazionale per la Fisica Matematica of C.N.R.     

Pressure measuring techniques in I.C.E.

Summary A revue of the possible errors affecting pressure measurements in internal combustion engines is presented. A new instrument based on the principle of the Balanced Pressure Indicator and signal multiplexing was developped. Its characteristics used both to obtain an accurate mean pressure diagram and to calibrate pressure transducers in working engines. The overall ability of obtaining meaningful pressure data was shown, even if it is clear that pressure measurements are more an art than a mere technique, given the complexity of the problems involved.

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Sommario L'articolo presenta un'analisi dei possibili errori che possono distorcere la misurazione delle pressioni nella camera di combustione dei motori a combustione interna. Un nuovo strumento, basato sul principio dell'indicatore di pressione a bilanciamento di pressioni e del multiplex a modi di impulsi, è qui anche presentato ed utilizzato sia per ottenere un diagramma medio di pressioni di notevole accuratezza, che per calibrare trasduttori di pressione in condizioni di lavoro, cioè mentre il motore è in funzione. Ne risulta che è possibile ottenere diagrammi di pressione veramente rappresentativi delle condizioni di lavoro del motore, anche se è chiaro che, data la complessità dei problemi relativi a detta misurazione, misurare la pressione nei motori è più un'arte che pura tecnica.

     

Direct numerical simulation of laminar breakdown in high-speed,axisymmetric boundary layers

The laminar breakdown of high-speed, axisymmetric boundary-layer flow is simulated numerically by solving the compressible Navier-Stokes equations using spectral collocation and high-order compact-difference techniques. Numerical test cases include Mach 4.5 flow along a hollow cylinder and Mach 6.8 flow along a sharp cone. From initial states perturbed by second-mode primary and subharmonic (H-type) secondary disturbances, the well-resolved (temporal) calculations proceed well into the laminar breakdown stages, characterized by saturation of the primary and secondary instability waves, explosive growth of higher harmonics, and rapid increase in the wall shear stress. The numerical results qualitatively replicate two previously unexplained phenomena which have been observed in high-speed transition experiments: the appearance of so-called rope-like waves and the precursor transition effect, in which transitional flow appears to originate near the critical layer well upstream of the transition location at the wall. The numerical results further reveal that neither of these effects can be explained, even qualitatively, by linear stability theory alone. Structures of rope-like appearance are shown to arise from secondary instability. Whereas certain features of the precursor transition effect also emerge from secondary instability theory, its nature is revealed to be fundamentally nonlinear.This research was accomplished largely while the first author was in residence as a National Research Council Associate at NASA Langley Research Center, Hampton, VA 23665, USA.     

Conical flows in the neighborhood of breaks in the edges of surfaces separating cocurrent supersonic streams of perfect gas

An investigation is made into the conical flows which occur when a perfect (inviscid and nonheat conducting) gas flows over the terminal edges of surfaces with breaks separating an external and an internal flow with velocity vectors parallel to the line of intersection of the surfaces. Such flows are observed, in particular, in the neighborhood of breaks in the outlet edge of a nozzle of rectangular cross section with a straight or skewed exit plane under conditions of underexpanded flow of a supersonic jet into a cocurrent supersonic stream. By means of a linear analysis flow patterns corresponding to various flow interaction regimes and edge geometries are constructed and a law of similarity is formulated. The validity of the results thus obtained is confirmed by examples of the numerical solution of the complete nonlinear system of Euler equations. In this connection, within the framework of the approach outlined in [1], as a rule, together with the shocks and characteristic surfaces bounding the conical flow in question, the shear discontinuity separating the external and internal streams is constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 119–127, January–February, 1935.     

Heat and entropy in nonextensive thermodynamics

The concepts of the quantity of heat and work are deduced in the context of non-extensive statistical mechanics, following steps parallel to those employed in extensive statistical mechanics.Received: 31 January 2003, Accepted: 6 May 2003, Published online: 21 November 2003PACS: 05.70.-a, 05.30.-d, 05.90. + m     

Closure of microcracks during unloading and the formation of reverse dislocations

Conclusion During unloading, local closure of the crack is followed by the emission of the first pair of reverse dislocations. The formation of an area of local contact during unloading occurs with a bang; the critical SIF of the external loads at this moment coincides with the value of the overall SIF of the field of the primary sessile dislocations. There is always a free gap between the crack tip and the area of local contact. External loads acting in the crack plane and not resulting in a stress concentration at the crack front play an important role in the emission of reverse dislocations (in particular, they may block their departure from the S-structure).Pacific Oceanological Institute, Academy of Sciences of the USSR, Vladivostok. Translated from Prikladnaya Mekhanika, Vol. 24, No. 7, pp. 3–18, July, 1988.     

An extension of Reiner's “Deborah Number” concept to a Wide field of rheological investigations

Summary Reiner defined a numeric, which he called theDeborah Number to represent the ratio of a relaxation time to a natural (observation) time. This implies aMaxwell model but is readily extended to complete relaxation spectra. Similar Numbers are proposed for retardation times and also for some conditions of coagulation thixotropy and for data from certain psychophysical experiments.