Design of an Axial Impulse Turbine for Enthalpy Drop Recovery

2014 ◽  
Author(s):  
Gaetano Morgese ◽  
Marco Torresi ◽  
Bernardo Fortunato ◽  
Sergio Mario Camporeale
Keyword(s):  
Industrial Process ◽  
Geometrical Parameters ◽  
Impulse Turbine ◽  
One Dimensional ◽  
Analytical Functions ◽  
Process Plants ◽  
The One ◽  
Definition Of ◽  
Turbine Design ◽  
Work Done

In industrial process plants, often there is the need to reduce the pressure of the operating flow. Generally this is performed by means of valves which expand the flow without any work done. The same operation could be performed by replacing these valves with turbines, with the advantage of energy recovery, hence improving the overall efficiency of the system. In this work, a simple and rapid method is shown in order to design a single stage, straight bladed, axial impulse turbine for enthalpy recovery. Assigned the desired flow rate and the minimum power output, the turbine design is performed according to a one-dimensional study into which loss effects are considered by means of appropriate coefficients. From the one-dimensional analysis the heights, the pitch angle, the inlet and outlet angles of both rotor and stator blades are obtained. Actually, the rotor and stator blade profiles are defined by means of several analytical functions. The blade design is then validated by means of CFD simulations. The definition of loss coefficients and blade geometrical parameters is clearly an iterative process, which needs to be repeated until convergence is reached. Furthermore, by means of fully 3D simulations, the effect of the rotor-stator distance is investigated in order to maximize the turbine performance.

scholarly journals Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

ACOUSTIC ATTENUATION CHARACTERISTICS OF STRAIGHT-THROUGH PERFORATED TUBE SILENCERS AND RESONATORS

2008 ◽  
Vol 16 (03) ◽  
pp. 361-379 ◽  
Author(s):  
Z. L. JI
Keyword(s):  
Performance Prediction ◽  
Transmission Loss ◽  
Three Dimensional ◽  
Geometrical Parameters ◽  
Mean Flow ◽  
Acoustic Attenuation ◽  
One Dimensional ◽  
The One ◽  
Attenuation Characteristics ◽  
Perforated Tube

The one-dimensional analytical solutions are derived and three-dimensional substructure boundary element approaches are developed to predict and analyze the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators without mean flow, as well as to examine the effect of nonplanar waves in the silencers and resonators on the acoustic attenuation performance. Comparisons of transmission loss predictions with the experimental results for prototype straight-through perforated tube silencers demonstrated that the three-dimensional approach is needed for accurate acoustic attenuation performance prediction at higher frequencies, while the simple one-dimensional theory is sufficient at lower frequencies. The BEM is then used to investigate the effects of geometrical parameters on the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators in detail.

Filtering performance and optimization of double-chamber compound hydraulic attenuators

2017 ◽  
Vol 232 (18) ◽  
pp. 3250-3262 ◽  
Author(s):  
Fan Yang ◽  
Bin Deng
Keyword(s):  
Insertion Loss ◽  
Pressure Pulsation ◽  
Low Frequency ◽  
Geometrical Parameters ◽  
Double Precision ◽  
Expansion Chamber ◽  
One Dimensional ◽  
Wave Region ◽  
The One ◽  
Double Chamber

At present, double expansion chamber structures are widely used in the field of acoustic attenuation, and two kinds of double-chamber compound structures for hydraulic attenuators are proposed in this paper. A one-dimensional analytical approach was developed to predict the pressure pulsation attenuation performance of these two structures, and comparisons of insertion loss predictions with experimental results illustrated that the one-dimensional approach is suitable for accurate prediction among the research frequency band. This approach was then used to investigate the effects of porosity and geometrical parameters on the pressure pulsation performance of these two double-chamber compound hydraulic attenuators. To optimize the pressure pulsation attenuation performance at the backwash frequency, parameter optimization was performed for these double-chamber compound structures, and a genetic algorithm based on double-precision floating-point encoding was proposed. The results showed that the range of attenuation frequency bands was widened; however, the effect on low frequency filtering characteristics was limited. The insertion loss of the second structure, which had a partially perforated tube, exhibits a superposition of dome attenuation and axial resonance in the plane wave region. By choosing the length and location of the perforated section to match resonances with the troughs of the pulsation attenuator, a desirable broadband pressure pulsation attenuation can be obtained.

Theory of thermal explosions with simultaneous parallel reactions I. Foundations and the one-dimensional case

1984 ◽  
Vol 393 (1804) ◽  
pp. 85-100 ◽  
Keyword(s):  
Activation Energy ◽  
Dimensionless Parameter ◽  
Exothermic Reactions ◽  
One Dimensional ◽  
Temperature Excess ◽  
Parallel Reactions ◽  
The One ◽  
Definition Of ◽  
Thermal Explosions ◽  
Thermal Explosion Theory

Many real, exothermic systems involve more than one simultaneous reaction. Even when they are chemically independent, interactions must arise through their several responses to the collective generation of heat. A simple and unifying approach is possible to the behaviour of such systems below and up to criticality. It introduces a communal activation energy E as the basis for dimensionless quantities ( θ, δ, ϵ and so on) but otherwise involves only familiar ideas from basic thermal explosion theory. The definition of E is E = RT 2 d (In Z )/d T , where Z = Ʃ Z i . Here, Z is the rate of energy release per unit volume (the power density) by the whole system and Z i is the contribution of the constituent i . This enables us to define and use the conventional dimensionless parameter δ for the whole system and for its constituent reactions. We illustrate affairs by considering a pair of concurrent, exothermic reactions; heat is transferred solely by conduction towards the faces (temperature T a ) of an infinite slab of thickness 2 a and conductivity k . For a constituent reaction ( i = 1, 2 here) δ i = ( Ea 2 / k RT 2 a ) Z i ( T a ) and for the whole system δ = δ 1 + δ 2 (+...) for two (or more) reactions. We find that the condition δ > δ cr guarantees instability, where δ cr is always less than 0.878. The bounds 0.65 < δ cr < 0.878 are good enough for a substantial range of relative sizes of activation energy 0.2 < E 1 / E 2 < 5. We also pursue the problem numerically and present solutions for critical δ and critical central temperature excess over the whole composition range for a pair of simultaneous exothermic reactions.

FINITE SYSTEMS ON PHASE SPACE

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1956-1967 ◽  
Author(s):  
KURT BERNARDO WOLF
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Hamiltonian Systems ◽  
Wigner Distribution ◽  
Wigner Distribution Function ◽  
Finite Fourier Transform ◽  
One Dimensional ◽  
Finite Systems ◽  
The One ◽  
Definition Of

This contribution summarizes work on finite, non-cyclic Hamiltonian systems —in particular the one-dimensional finite oscillator—, in conjunction with a Lie algebraic definition of the (meta-) phase space of finite systems, and a corresponding Wigner distribution function for the state vectors. The consistency of this approach is important for the strategy of fractionalization of a finite Fourier transform, and the contraction of finite unitary to continuous symplectic transformations of Hamiltonian systems.

scholarly journals Thermal processes in natural gas pipeline transport

2020 ◽  
Vol 16 (3) ◽  
pp. 260-266
Author(s):  
Vladimir A. Suleymanov ◽  
◽  
Keyword(s):  
Thermal Energy ◽  
Gas Flow ◽  
Gas Pipeline ◽  
Friction Forces ◽  
One Dimensional ◽  
Natural Gas Pipeline ◽  
Longitudinal Temperature ◽  
The One ◽  
Definition Of

A commonly used premise in pipeline hydraulics where the work of friction forces performed at the movement of real gas in the gas pipeline completely turns into thermal energy is verified in the article. By means of the integral definition of Clausius entropy, it is shown that the premise of the conversion of friction forces into thermal energy of gas flow is justified with an acceptable accuracy for engineering applications in relation to the one-dimensional formulation of the task regarding the determination of the longitudinal temperature field of gas.

scholarly journals Technical note: rectifying systematic underestimation of the specific energy required to evaporate water into the atmosphere

2018 ◽  
Author(s):  
Andrew S. Kowalski
Keyword(s):  
Specific Energy ◽  
Technical Note ◽  
Water Molecules ◽  
Specific Work ◽  
Surface Boundary ◽  
One Dimensional ◽  
The One ◽  
Virtual Temperature ◽  
Work Done ◽  
Latent Heat Of Vaporization

Abstract. Not all of the specific energy consumed when evaporating water into the atmosphere (λ) is due to the latent heat of vaporization (L). What L represents is the specific energy necessary to overcome affinities among liquid water molecules, neglecting the specific work done against atmospheric pressure (p) when water expands in volume (V) from liquid to gas (pV work). Here, in the one-dimensional context typifying micrometeorology, the pV work done in such an expansion is derived based on the Stefan flow velocity at the surface boundary, yielding a simple function of the virtual temperature; additionally, an empirical formula is provided that approximates λ quite accurately over a useful range of environmental conditions. Neglect of this pV work term has caused a systematic 3–4 % underestimation of λ, and to some extent inhibited closure of the surface energy balance.

The Formation of a Shock Wave in a Blade Passage of a Partial Admission Turbine

1968 ◽  
Vol 90 (4) ◽  
pp. 555-562 ◽  
Author(s):  
W. A. Woods ◽  
F. Kuo-Hua Chu ◽  
R. W. Mann
Keyword(s):  
Shock Wave ◽  
Supersonic Nozzle ◽  
Theoretical Work ◽  
Dimensional Theory ◽  
Impulse Turbine ◽  
Blade Passage ◽  
One Dimensional ◽  
Partial Admission ◽  
The One ◽  
Hydraulic Analogy

The problem of unsteady flow in the blade passage of a partial admission impulse turbine with supersonic nozzle flow is introduced. Previous work carried out at M.I.T. revealed the presence of a shock wave at the entrance to the blade passages and this report sets out to predict the formation of such a shock wave using a one-dimensional theory. The one-dimensional theory is discussed in some detail and a novel method for dealing with the inflow boundary conditions is developed. Details of a characteristic calculation are given, and this is matched with a shock wave analysis to predict the formation of the shock wave. The implications of the theoretical work are discussed and experimental results obtained from a hydraulic analogy are presented which confirm the analysis.

Effective aperture of X-ray compound refractive lenses

2017 ◽  
Vol 24 (3) ◽  
pp. 609-614 ◽  
Author(s):  
V. G. Kohn
Keyword(s):  
Integral Intensity ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
The Real ◽  
A Value ◽  
Effective Aperture ◽  
The One ◽  
Definition Of ◽  
Focusing Properties

A new definition of the effective aperture of the X-ray compound refractive lens (CRL) is proposed. Both linear (one-dimensional) and circular (two-dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76, 600–603; (2003). J. Exp. Theor. Phys. 97, 204–215; (2009). J. Surface Investig. 3, 358–364; (2012). J. Synchrotron Rad. 19, 84–92; Kohn et al. (2003). Opt. Commun. 216, 247–260; (2003). J. Phys. IV Fr, 104, 217–220], the FWHM of the X-ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6, 1153–1167; (1998). J. Appl. Phys. 84, 5855–5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two-dimensional CRL is proposed which allows one to calculate the two-dimensional CRL through the one-dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.

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