scholarly journals A new design method for high conditions applied to minimum length nozzles

2021 ◽  
Vol 33 ◽  
pp. 134-151
Author(s):  
Mohamed Roudane ◽  
Merouane Salhi ◽  
Ahmed Boucherit
Keyword(s):  
Initial Conditions ◽  
Design Method ◽  
Molecular Size ◽  
State Equation ◽  
Minimum Length ◽  
Real Gas ◽  
The Real ◽  
Finite Differences Method ◽  
Linear Differential ◽  
The One

This present work focused on new nozzles design method, based on the characteristics method, which is a technique method to reduce a partial differential equation to linear differential equations along which the solution can be integrated from initial conditions. The latter is developed under the real gas theory, because when the both pressure and temperature of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect, and it becomes a real gas. The presented equations of the characteristics remain valid whatever area or field of study. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The resolution has been made by the finite differences method using the corrector predictor algorithm. As result, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature HT models on the one hand and our results by the real gas theory on the other of nozzles are made. An important gain of length and weight can rise up to 40% and 20% respectively. It is in this context that Minimum Length Nozzle (MLN) nozzles for aerospace engines based on real gas theory were developed to achieve maximum thrust with the smallest possible nozzle weight (minimum length).

Stagnation pressure effect on Prandtl Meyer function for air

2016 ◽  
Vol 231 (2) ◽  
pp. 326-337 ◽  
Author(s):  
Merouane Salhi ◽  
Toufik Zebbiche ◽  
Abderrahmane Mehalem
Keyword(s):  
High Temperature ◽  
Pressure Effect ◽  
Molecular Size ◽  
State Equation ◽  
Stagnation Pressure ◽  
Intermolecular Force ◽  
Perfect Gas ◽  
Real Gas ◽  
New Form ◽  
Made In

When the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not stay perfect. Its state equation change and it becomes for a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. The aim of this work is developing a new form of Prandtl Meyer function based on those assumptions; and determining the effect of stagnation pressure on this function. With the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The application is for air. A computation of error was made in this case to give a limit of the perfect gas and the high temperature models compared to the real gas model.

scholarly journals The Diagonalization Paradox - Expanded

2020 ◽  
Author(s):  
Ron Ragusa
Keyword(s):  
Initial Conditions ◽  
Georg Cantor ◽  
Natural Numbers ◽  
Real Numbers ◽  
The Real ◽  
One To One ◽  
The One

In 1891 Georg Cantor published his Diagonal Method which, he asserted, proved that the real numbers cannot be put into a one-to-one correspondence with the natural numbers. In this paper we will see how by varying the initial conditions of Cantor’s proof we can use the diagonal method to produce a one-to-one correspondence between the set of natural numbers and the set of infinite binary decimals in the interval (0, 1). In the appendix we demonstrate that using the diagonal method recursively will, at the limit of the process, fully account for all the infinite binary decimals in (0, 1). The proof will cement the one-to-one correspondence between the natural numbers and the infinite binary decimals in (0, 1).

Stagnation pressure effect on the supersonic flow parameters with application for air in nozzles

2016 ◽  
Vol 120 (1224) ◽  
pp. 313-354 ◽  
Author(s):  
Merouane Salhi ◽  
Toufik Zebbiche ◽  
Abderrahmane Mehalem
Keyword(s):  
Supersonic Flow ◽  
Supersonic Nozzle ◽  
Molecular Size ◽  
State Equation ◽  
Stagnation Pressure ◽  
Design Parameters ◽  
Perfect Gas ◽  
Thrust Coefficient ◽  
Real Gas ◽  
Flow Parameters

ABSTRACTWhen the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas doesn't stay perfect. Its state equation changes and it becomes a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation. The aim of this work is to determine the effect of stagnation pressure on the thermodynamic, physical and geometrical supersonic flow parameters in order to find a general form for real gas. With the assumptions that Berthelot's state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The design parameters of the supersonic nozzle-like thrust coefficient depend directly on the stagnation parameters of the combustion chamber. The application made for air. A computation of error was made in this case to give a limit of the perfect gas model compared to the real gas model.

ON THE THERMODYNAMICAL STABILITY OF THE PLASMA OF GAS DISCHARGE IN THE REAL GAS

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-677-C7-678
Author(s):  
S. W. Temko ◽  
K. W. Temko ◽  
S. K. Kuzmin
Keyword(s):  
Gas Discharge ◽  
Real Gas ◽  
The Real

Hidden “holes” in the capital of banks and the supply of credit to the real sector of economy

2018 ◽  
pp. 49-68 ◽  
Author(s):  
M. E. Mamonov
Keyword(s):  
Credit Risk ◽  
The Other ◽  
Real Sector ◽  
Capital Management ◽  
Loan Loss ◽  
Short Term ◽  
The Real ◽  
Ex Post ◽  
The One

Our analysis documents that the existence of hidden “holes” in the capital of not yet failed banks - while creating intertemporal pressure on the actual level of capital - leads to changing of maturity of loans supplied rather than to contracting of their volume. Long-term loans decrease, whereas short-term loans rise - and, what is most remarkably, by approximately the same amounts. Standardly, the higher the maturity of loans the higher the credit risk and, thus, the more loan loss reserves (LLP) banks are forced to create, increasing the pressure on capital. Banks that already hide “holes” in the capital, but have not yet faced with license withdrawal, must possess strong incentives to shorten the maturity of supplied loans. On the one hand, it raises the turnovers of LLP and facilitates the flexibility of capital management; on the other hand, it allows increasing the speed of shifting of attracted deposits to loans to related parties in domestic or foreign jurisdictions. This enlarges the potential size of ex post revealed “hole” in the capital and, therefore, allows us to assume that not every loan might be viewed as a good for the economy: excessive short-term and insufficient long-term loans can produce the source for future losses.

scholarly journals A novel approach to the computation of one-loop three- and four-point functions: I. The real mass case

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
J Ph Guillet ◽  
E Pilon ◽  
Y Shimizu ◽  
M S Zidi
Keyword(s):  
Building Blocks ◽  
The Real ◽  
Alternative Method ◽  
Novel Approach ◽  
Reduction Methods ◽  
Real Mass ◽  
Novel Method ◽  
Algebraic Reduction ◽  
The One ◽  
Mass Case

Abstract This article is the first of a series of three presenting an alternative method of computing the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following ’t Hooft and Veltman adopted previously. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the three-point functions and, in a similar way, to the four-point functions. It also extends to complex masses without much complication. Lastly, it extends to kinematics more general than that of the physical, e.g., collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.

PP469 From Theory To Practice: Which Value Framework Is Applied For Onco-Hematology Therapies In Italy? A 5-year Retrospective Analysis

2020 ◽  
Vol 36 (S1) ◽  
pp. 37-37
Author(s):  
Americo Cicchetti ◽  
Rossella Di Bidino ◽  
Entela Xoxi ◽  
Irene Luccarini ◽  
Alessia Brigido
Keyword(s):  
Real World ◽  
Ad Hoc ◽  
Grey Literature ◽  
National Level ◽  
Pharmaceutical Products ◽  
European Medicines Agency ◽  
The Real ◽  
R Process ◽  
The One ◽  
The Impact

IntroductionDifferent value frameworks (VFs) have been proposed in order to translate available evidence on risk-benefit profiles of new treatments into Pricing & Reimbursement (P&R) decisions. However limited evidence is available on the impact of their implementation. It's relevant to distinguish among VFs proposed by scientific societies and providers, which usually are applicable to all treatments, and VFs elaborated by regulatory agencies and health technology assessment (HTA), which focused on specific therapeutic areas. Such heterogeneity in VFs has significant implications in terms of value dimension considered and criteria adopted to define or support a price decision.MethodsA literature research was conducted to identify already proposed or adopted VF for onco-hematology treatments. Both scientific and grey literature were investigated. Then, an ad hoc data collection was conducted for multiple myeloma; breast, prostate and urothelial cancer; and Non Small Cell Lung Cancer (NSCLC) therapies. Pharmaceutical products authorized by European Medicines Agency from January 2014 till December 2019 were identified. Primary sources of data were European Public Assessment Reports and P&R decision taken by the Italian Medicines Agency (AIFA) till September 2019.ResultsThe analysis allowed to define a taxonomy to distinguish categories of VF relevant to onco-hematological treatments. We identified the “real-world” VF that emerged given past P&R decisions taken at the Italian level. Data was collected both for clinical and economical outcomes/indicators, as well as decisions taken on innovativeness of therapies. Relevant differences emerge between the real world value framework and the one that should be applied given the normative framework of the Italian Health System.ConclusionsThe value framework that emerged from the analysis addressed issues of specific aspects of onco-hematological treatments which emerged during an ad hoc analysis conducted on treatment authorized in the last 5 years. The perspective adopted to elaborate the VF was the one of an HTA agency responsible for P&R decisions at a national level. Furthermore, comparing a real-world value framework with the one based on the general criteria defined by the national legislation, our analysis allowed identification of the most critical point of the current national P&R process in terms ofsustainability of current and future therapies as advance therapies and agnostic-tumor therapies.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

1996 ◽  
Vol 324 ◽  
pp. 163-179 ◽  
Author(s):  
A. Levy ◽  
G. Ben-Dor ◽  
S. Sorek
Keyword(s):  
Porous Materials ◽  
Initial Conditions ◽  
Computer Code ◽  
Experimental Results ◽  
Numerical Code ◽  
Materials Development ◽  
Numerical Predictions ◽  
Wide Range ◽  
Dimensional Version ◽  
The One

The governing equations of the flow field which is obtained when a thermoelastic rigid porous medium is struck head-one by a shock wave are developed using the multiphase approach. The one-dimensional version of these equations is solved numerically using a TVD-based numerical code. The numerical predictions are compared to experimental results and good to excellent agreements are obtained for different porous materials and a wide range of initial conditions.

A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

1986 ◽  
Vol 102 (3-4) ◽  
pp. 253-257 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Linear Differential Equation ◽  
Asymptotic Series ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Real ◽  
Linear Differential ◽  
Image Position

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then

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