The Effect of Shock Waves on the Isentropic Efficiency of Convergent— Divergent Nozzles

1958 ◽  
Vol 62 (569) ◽  
pp. 377-382
Author(s):  
B. W. Martin ◽  
F. J. Bayley
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Back Pressure ◽  
Normal Shock ◽  
Specific Heats ◽  
Plane Normal ◽  
Design Value ◽  
Set Up ◽  
Isentropic Efficiency ◽  
Oblique Shocks

Now a Days, the phenomenon is well known of the plane normal shock waves set up in the divergent section of a convergent-divergent nozzle, and the oblique shocks which occur in the resultant jet downstream of the nozzle exit when operating under overall pressure ratios less than the design value. Stodola was among the first to demonstrate experimentally the effect on the flow within the nozzle of increasing the back pressure above the design value, and work by Schmidt, Martin) and others, has been concerned with the theoretical changes in pressure, temperature, density and Mach number across a normal shock wave whose position varies along the nozzle axis. The effect of working substance on these changes, which is taken into account by the ratio of specific heats, has also been investigated.

Normal Shock Wave Phenomena in a Convergent-Divergent Nozzle

1953 ◽  
Vol 57 (511) ◽  
pp. 455-460 ◽  
Author(s):  
B. W. Martin
Keyword(s):  
Shock Wave ◽  
Common Ground ◽  
Back Pressure ◽  
Normal Shock ◽  
Normal Shock Wave ◽  
Specific Heats ◽  
Nozzle Axis ◽  
Set Up ◽  
Wave Phenomena ◽  
Approach Unity

SummaryIn recent years, aerodynamics and thermodynamics have found common ground in the specialised field of gas dynamics. Developments in this subject have led to a much more complete and widespread knowledge of subsonic, sonic and supersonic flow of gases in the conventional type of convergent-divergent nozzle. When the back pressure is raised above the value against which the nozzle is designed to discharge, oblique and then normal shock waves are set up in the divergent cone at a position along the nozzle axis determined by the magnitude of that back pressure. The gas which has crossed the shock wave is subjected to a process of subsonic compression.In this paper a theoretical investigation is made of the changes in pressure, temperature, density and Mach number which occur across a normal shock wave, when the position of the wave varies along the nozzle axis. The investigation illustrates the effect of change of medium, for which the relevant property is the ratio of specific heats. This ratio for certain polyatomic gases may approach unity (e.g. for Dichlorodifluoromethane CCl2F2, in gaseous form, γ=1·06), and for the inert monatomic gases γ= 1·667. The analysis is made non-dimensional by expressing such quantities as gas pressure, temperature, and density at any given position along the nozzle axis relative to the values of the particular parameter at entry to the convergent section.

scholarly journals A Steam Ejector Refrigeration System Powered by Engine Combustion Waste Heat: Part 2. Understanding the Nature of the Shock Wave Structure

2019 ◽  
Vol 9 (20) ◽  
pp. 4435 ◽  
Author(s):  
Yu Han ◽  
Xiaodong Wang ◽  
Lixin Guo ◽  
Anthony Chun Yin Yuen ◽  
Hengrui Liu ◽  
...  
Keyword(s):  
Shock Wave ◽  
Waste Heat ◽  
Wave Structure ◽  
Back Pressure ◽  
Normal Shock ◽  
Engine Fuel ◽  
Refrigeration System ◽  
Shock Wave Structure ◽  
Steam Ejector ◽  
Shock Region

In general, engine fuel combustion generates 30% waste heat, which is disposed to the environment. The use of the steam ejector refrigeration to recycle the waste heat and transfer them to useful energy source could be an environmentally friendly solution to such an issue. The steam ejector is the main component of the ejector refrigeration system, which can operate at a low-temperature range. In this article, the internal shock wave structure of the ejector is comprehensively studied through the computation fluid dynamics (CFD) approach. The shock wave structure can be subdivided into two regions: firstly the pseudo-shock region consisting of shock train and co-velocity region; secondly the oblique-shock region composed of a single normal shock and a series of oblique shocks. The effect of the shock wave structure on both pumping performance and the critical back pressure were investigated. Numerical predictions indicated that the entrainment ratio is enhanced under two conditions including (i) a longer pseudo-shock region and (ii) when the normal shock wave occurs near the outlet. Furthermore, the system is stabilized as the back pressure and its disturbance is reduced. A critical range of the primary fluid pressure is investigated such that the pumping is effectively optimized.

Numerical Investigation of Cloud Cavitation and Its Induced Shock Waves

2021 ◽  
Author(s):  
Takahiro Ushioku ◽  
Hiroaki Yoshimura
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Multiphase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lagrangian Description ◽  
Cloud Cavitation ◽  
Wave Emission ◽  
Set Up ◽  
Unsteady Behavior

Abstract This paper numerically investigates unsteady behavior of cloud cavitation, in particular, to elucidate the induced shock wave emission. To do this, we consider a submerged water-jet injection into still water through a nozzle and make some numerical analysis of two-dimensional multiphase flows by Navier-Stokes equations. In our previous study [7], we have shown that twin vortices symmetrically appear in the injected water, which plays an essential role in performing the unsteady behavior of a cloud of bubbles. In this paper, we further illustrate the elementary process of the emission of the shock waves. First, we set up the mixture model of liquid and gas in Lagrangian description by the SPH method, together with the details on the treatment of boundary conditions. Second, we show the velocity fields of the multiphase flow to illustrate the inception, growth as well as the collapse of the cloud. In particular, we explain the mechanism of the collapse of the cloud in view of the motion of the twin vortices. Further, we investigate the pressure fields of the multiphase flow in order to demonstrate how the shock wave is emitted associated with the collapse of the cloud. Finally, we show that a small shock wave may be released prior to the main shock wave emission.

Dusty Shock Waves

1988 ◽  
Vol 41 (11) ◽  
pp. 379-437 ◽  
Author(s):  
O. Igra ◽  
G. Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Flow Field ◽  
Gaseous Medium ◽  
Present Review ◽  
Normal Shock ◽  
Dusty Gas ◽  
Perfect Gas ◽  
Post Shock ◽  
Dusty Shock Waves

The flow field developed behind shock waves in a pure gaseous medium is well known and documented in all gasdynamics textbooks. This is not the case when the gaseous medium is seeded with small solid particles. The present review treats various cases of shock waves propagation into a gas-dust suspension (dusty shock waves). It starts (chapter 1) with basic definitions of two-phase (gas-dust) suspensions and presents a general form of the conservation equations which govern dusty shock wave flows. In chapter two, the simple case of a steady flow of a suspension consisting of an inert dust and a perfect gas through a normal shock wave is studied. The effect of the dust presence, and of changes in its physical parameters, on the post-shock wave flow are discussed. Obviously, these discussions are limited to relatively weak shock waves (perfect gas). For stronger normal shock waves, the assumption of a perfect gas no longer holds. Therefore, in chapter three, real gas effects (ionization or dissociation) are taken into account when calculating the post-shock flow field. In chapter four, the dust chemistry is included and its effects on the post-shock flow is studied. In order to emphasize the role played by the dust chemistry, a comparison between a reactive and a similar inert suspension is presented. The case of an oblique shock wave in a dusty gas is discussed in chapter five. In all cases treated in chapters two to five the flow is steady; however, in many engineering applications this is not the case. In reality, even for the simplest case of a one-dimensional flow (normal shock wave propagation into quiescent suspension—the dusty shock tube) the shock wave attenuates and the flow field behind it is not steady. This case is treated in chapter six. The cases treated in chapters two to six deal with planar shock waves. However, all explosion generated shock waves in the atmosphere are spherical. Due to the engineering importance of this case, the post-shock flow for spherical shock waves in a dusty gas is studied, in detail, in chapter seven. It is shown in the present review that the dust presence has significant effects on the post-shock flow field. In all cases studied, a relaxation zone is developed behind the shock wave front. Throughout this zone momentum and energy exchange between the two phases of the suspension takes place. Through these interactions a new state of equilibrium is reached. The extent of the relaxation zone depends upon the dust loading ratio, the dust particle diameter, its specific heat capacity, and the dust spatial density. Due to the complexity of conducting experimental investigations with dusty shock waves, the number of published experimental results is very limited. As a result most of the present review contains numerical studies. However, in the few cases where experimental data are available, (e.g. dusty shock tube flow; see chapter six) a comparison between the numerical and experimental results is given.

Analysis of Normal Shock Waves in Particle Laden Gas

1964 ◽  
Vol 86 (4) ◽  
pp. 655-664 ◽  
Author(s):  
A. R. Kriebel
Keyword(s):  
Shock Wave ◽  
Particle Size ◽  
Shock Waves ◽  
Solid Propellant ◽  
Weak Shock ◽  
Normal Shock ◽  
Wave Measurements ◽  
Solid Propellant Rocket ◽  
Propellant Rocket ◽  
Motor Exhaust

The internal structure of a normal shock wave in a perfect gas heavily laden with particles having a distribution of sizes is machine computed by numerical integration. The results of a small-perturbation analysis for weak shock waves and one particle size compare well with the machine-computed results for these restricted conditions. Both methods indicate that the thickness of weak shock waves increases in proportion to the particle size squared and inversely with the shock strength. For conditions typical of solid propellant-rocket motor exhaust streams the computed shock-wave thickness is several inches. With such computed results both the amount and the size distribution of suspended particles can be found individually from shock-wave measurements.

Propagation of spherical shock waves in stars

1956 ◽  
Vol 1 (4) ◽  
pp. 436-453 ◽  
Author(s):  
Akira Sakurai
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Power Series ◽  
Present Author ◽  
Finite Energy ◽  
Velocity Of Sound ◽  
Specific Heats ◽  
Fundamental Significance ◽  
Spherical Shock ◽  
Central Explosion

Propagation of spherical shock waves through self-gravitating polytropic gas spheres such as stars, caused by an instantaneous central explosion of finite energy E, is discussed theoretically. The problem is characterized by two lengths R0, L, where $R_0 = \left(\frac {E}{4\pi p_0}\right)^{1|3},\;\;\;\;\; L = \left(\frac {3C^2_0}{2\pi \rho_0G} \right)^{1|2}$p0 and C0 are the values of pressure, density and velocity of sound at the centre of the equilibrium pre-explosion state, and G is the constant of gravitation. R0 and L are scales connected with the power of the explosion and the dimensions of the star respectively, and their ratio A = R0/L has a fundamental significance. A solution especially suitable in the case of A = O(1) is developed in the form of power series in R/R0 (R is the distance between the shock front and the centre) by a method similar to that used in previous papers by the present author (1953, 1954). An approximation to this solution is carried out up to the term in R3. In particular, the velocity of the shock wave U is found to be $\frac {U}{C_0} = 1\cdot30 \left(\frac{R}{R_0}\right)^{-3|2} \{1 +0\cdot41A^2\left(\frac{R}{R_0}\right)^2 + 0\cdot 57\left(\frac{R}{R_0}\right)^3 +\ldot\}$ for the case of λ = 1.4, where λ is the ratio of specific heats.

scholarly journals Numerical investigation of the thermal-caloric imperfections on entropy enhancement across normal shock waves

2020 ◽  
Vol 48 (4) ◽  
pp. 285-308
Author(s):  
MEROUANE SALHI
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Molecular Size ◽  
Ideal Gas ◽  
Normal Shock ◽  
Wave Flow ◽  
Appreciable Effect ◽  
Real Gas ◽  
Normal Shock Wave ◽  
The Impact

Changes in flow properties across a normal shock wave are calculated for a real gas, thus giving us a better affinity to the real behavior of the waves. The purpose of this work is to develop shock-wave theory under the gaseous imperfections. Expressions are developed for analyzing the supersonic flow of such a thermally and calorically imperfect gas. The effects of molecular size and intermolecular attraction forces are used to correct a state equation, focusing on determination of the impact of upstream stagnation parameters on a normal shock wave. Flow through a shock wave in air is investigated to find a general form for normal shock waves. At Mach numbers greater than 2.0, the temperature rise is considerably below, and hence the density rise is well above, that predicted assuming ideal gas behavior. It is shown that caloric imperfections in air have an appreciable effect on the parameters developed in the processes considered. Computation of errors between the present model based on real gas theory and a perfect gas model shows that the influence of the thermal and caloric imperfections associated with a real gas is important.

NUMERICAL SIMULATIONS OF INVISCID AIRFLOWS IN RAMJET INLETS

2009 ◽  
Vol 33 (2) ◽  
pp. 271-296 ◽  
Author(s):  
M. Akbarzadeh ◽  
M. J. Kermani
Keyword(s):  
Numerical Simulations ◽  
Heat Rate ◽  
Artificial Viscosity ◽  
Back Pressure ◽  
Normal Shock ◽  
Nozzle Throat ◽  
Flux Limiter ◽  
Fluent Software ◽  
Oblique Shocks ◽  
Good Agreement

The performances of three different ramjet inlets and an entire ramjet are numerically studied in this paper. The fluid is assumed to be inviscid. Inlet 1 is a SCRAMJET inlet and is chosen from the literature. Inlets 2 and 3 are instead designed based on the Oswatitsch principle. Inlets 2 and 3 produce a series of oblique shocks merging at the engine cowl lip followed by a terminating normal shock just downstream of the inlet throat. In ramjet, the combustion is modeled using a non-uniform volumetric heat source distributed in the combustor area. The position of the terminating normal shock in Inlets 2 and 3 is controlled via the inlet’s back pressure. Instead, in ramjet it is bounded by the amount of heat rate added in combustor and the exhaust nozzle throat area. For the numerical simulations, the Roe (1981) and MacCormack (1969) schemes are used. To prevent the spurious numerical oscillations in high resolution computations by Roe scheme the van Albada flux limiter (1982) is used, while in MacCormack scheme artificial viscosity terms are added to damp the oscillations. To double check the accuracy of the computations, the Fluent software package has also been used. Comparisons show very good agreement.

Investigation of shock-wave deformation history from recovered structure

1986 ◽  
Vol 44 ◽  
pp. 434-435
Author(s):  
M.A. Mogilevsky ◽  
L.S. Bushnev
Keyword(s):  
Shock Wave ◽  
Plastic Deformation ◽  
Dislocation Density ◽  
Shock Waves ◽  
Shock Front ◽  
Single Crystals ◽  
Residual Deformation ◽  
Deformation Structure ◽  
Deformation History ◽  
Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

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