# Mach number conditions

Descriptions of various MHD generator flow models can be found in the Hterature (28—30). A typical procedure for performing actual channel calculations (29) is to start by specifying the composition of the reactants, from which therm ochemical, thermodynamic, and electrical properties of the working fluid are generated (31). The principal input data required to proceed with the calculations are the total mass flow rate, the combustor stagnation pressure and enthalpy, and specified design conditions of magnetic field, electrical load parameter, and Mach number along the channel. It is implicitly assumed that the magnetic field can in fact be treated as a prescribed quantity, ie, it is not significantly influenced by the induced currents in the gas. More sophisticated, two- and three-dimensional computer codes have been developed to treat aspects of channel flow (32,33). Codes which can treat unsteady flows have also been developed for the analysis of end effects, transient flows, and flows with shock waves, and to determine conditions under which secondary flows or instabiUties may occur. [c.418]

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. [c.649]

Figure 6-5 (a) shows the special case of axial outflow, associated with a single-stage fan with a stator row preceding the rotor. This case has no residual whirl velocity at the exit. As a multistage design, it offers the advantage of acceleration in the stator, since R > 1, which has the effect of smoothing out the flow and providing the best possible conditions for the rotor. However, it has the disadvantage of having a very high relative velocity, Vri, and possibly a high Mach number. It is, therefore, unsuited for the first stage of the compressor, where Vg and u are high and the temperature is at its lowest, but may be more suited for the later stages where the Mach number may be lower. [c.230]

Any effect of Mach number is experienced by rotor and stator equally and thus neither (or both) are limiting, and this Mach number will be lower than for other degrees of reaction under the conditions stated. If equal lift and drag are assumed in both rotor and stator, then optimum efficiency is obtained with R = 0.5 and VJu = 0.5. Although the latter is not always true, it does provide a useful criterion. Furthermore, the blade angles are similar in rotor and stator, which may be an advantage in the [c.231]

A piston Mach number may be related to a flame Mach number if, under the condition of low overpressure, the mass enclosed by the piston flow field is equated to the mass enclosed by a flame flow field [c.94]

A simple method to estimate the overpressure generated by eonstant-velocity flames was suggested by Strehlow (1975) a summary follows. The change in density over a propagating flame front dependent on flame speed, Mach number, and energy addition is fully described by the jump conditions for a flame front. The change in density over the leading shock dependent on shock Mach-number is described by shock-jump conditions. Now the problem can be solved by relating the flame Mach number and the shock Mach number. [c.101]

Knowledge of RON and MON, or their combination, is not enough to predict the real behavior of a motor fuel in a mass-production engine. In fact for this case, the change in pressure and temperature as a function of time in gases under knocking conditions is usually very different from that observed in the CFR engine. Complementary experiments on the vehicle are necessary to find the correlations between the characteristics of the motor fuel (RON, MON, composition by chemical family) and its real behavior. This approach has caused the concept of Road octane number — a discussion of which would be too lengthy to describe here. However we will give the general trends which can be brought to light. [c.199]

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. [c.239]

However, it is expected that this situation will change, since a number of novel "non-invasive NDT techniques are now becoming available. With some of these techniques, the time required for a shutdown can be reduced. Other techniques make it possible to perform inspections whilst the installation is in full service. It is obvious that the availability of such techniques could support the knowledge already available on operational parameters and degradation mechanisms, in order to base shutdown intervals on actual plant condition. [c.949]

For biomolecular systems, the protein under consideration is placed in the center of a box of explicitly defined water molecules. This box is normally regular (all angles are equal to 90", but other geometries, e.g., a truncated octahedron, can be used also) and surrounded by its periodic images. Therefore, the box of real water molecules no longer has a border with the vacuum, which reduces related artifacts and additionally improves the bulk properties of the simulated solvent. To conserve the number of atoms (i.e., the total mass) in the system, a water molecule leaving the real box must be added again. One very important condition for periodic boundary calculation is that an atom of the real molecule must not interact with another real atom and its image at the same time (minimum image convention). For that reason, spherical cutoffs for the non-bonding interactions shotild be defined which have to be smaller than half the smallest box dimension. [c.366]

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. [c.369]

A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. [c.149]

CO—C H,—CO—0—CHj—CHOH—CHj—OOC—CgH,—CO— These are comparatively soft materials and they are soluble in a number of organic solvents. Under more drastic conditions (200-220°) and with a larger proportion of phthahc anhydride, the secondary alcohol groups are esterified and the simple chains become cross-hnked three dimensional molecules of much higher molecular weight are formed [c.1018]

The application of molecular dynamics to liquids or solvent-solute systems allows the computation of properties such as diffusion coefficients or radial distribution functions for use in statistical mechanical treatments. A liquid is simulated by having a number of molecules (perhaps 1000) within a specific volume. This volume might be cube, a parallelepiped, or a hexagonal cylinder. Even with 1000 molecules, a significant fraction would be against the wall of the box. In order to avoid such severe edge effects, periodic boundary conditions are used to make it appear as though the fluid is infinite. Actually, the molecules at the edge of the next box are a copy of the molecules at the opposite edge of the box. These simulations are discussed in more detail in Chapter 39. [c.64]

A liquid is simulated by having a number of molecules (perhaps 1000) within a specific volume. This volume might be a cube, parallelepiped, or hexagonal cylinder. Even with 1000 molecules, a significant fraction would be against the wall of the box. In order to avoid such severe edge effects, periodic boundary conditions are used to make it appear as though the fluid is infinite. Actually, the molecules at the edge of the next box are a copy of the molecules at the opposite edge of the box, as shown in Figure 39.1. [c.303]

As the voltage across the discharge is increased, the glow discharge gets brighter and the current rises as more and more electrons are released through ionization and through bombardment of the cathode by more ions. The negative glow is then almost on top of the cathode the separation between it and the cathode itself is much less than a millimeter. The positive column or plasma glow increases as the plasma spreads to occupy almost all of the space between the electrodes. At some point, the cathode glow suddenly becomes a bright spot on the cathode, and the voltage falls as the current flow increases again. This is when an arc is struck. There is a very bright narrow column of hot gas between the electrodes. The fairly sudden increase in the flow of electrons as the arc is struck probably arises from three sources. One is an increase in the numbers of secondary electrons emitted from the cathode under increased bombardment from the larger number of positive ions being produced. Another is increased thermal emission of ions as the cathode heats up, and a third is field emission (see Chapter 5 for information on field ionization). As the negative glow approaches ever nearer (10 m) to the cathode, the electric-field gradient between the cathode and the glow becomes very high, reaching 10 to 10 V/m for an applied potential of 100 V. This electric-field condition is in the region of that required for field ionization. [c.37]

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. [c.342]

In the propagation reaction, the monomer molecule reacts with an existing free-radical polymer chain end to make the chain one repeat unit longer. The polymer chains have two active ends, and they grow from both ends at the same time. Under normal coating conditions, the consumption of monomer by propagation must be much higher than its consumption by initiation to obtain high molecular weight polymer. In fact, the number-average molecular weight is determined by the proportion of monomer consumed by the two reactions, and is diminished by increases in deposition temperature or monomer partial pressure. [c.433]

They-function is a definite integral of an expression including Jq, the modified Bessel function of the first kind, y-function curves use stoichiometric time and the number of theoretical stages as the two parameters to fit breakthrough curves and extend to other conditions. These curves have been approximated for use on PC microcomputers (108). A phenomenological model requires the deterrnination of two parameters, a transfer coefficient, and a linear isotherm constant, from a complete breakthrough curve. The solution to the model is in an infinite series form, which is calculable by a hand-held calculator or personal computer (109). Another method separates the equiUbrium from the kinetic effects by constmcting effective equiUbrium curves. Because the solution to the model involves nonlinear algebraic or differential equations, graphs called solution charts are used to predict breakthrough fronts (110). Theoretical stages form the essence of the discrete cell model graphical procedures, which are appHed to flat isotherms and incorporate pore diffusivity and axial dispersion (98). Another solution technique is the use of fast Eourier transforms. Linear isotherms are required, but their appHcabiUty for predicting breakthrough curves has been demonstrated for isothermal and nonisothermal adsorbers (111). Another model, with a solution in infinite series form, incorporates separate mass-transfer coefficients for external film, macropore, and micropore resistances (112). Techniques have also been developed to predict breakthrough from fluidized beds. The behavior of organic solvents adsorbed from air on activated carbon was shown to exhibit breakthrough times that can be correlated to the adsorption capacity and the amount of bed expansion (113). [c.286]

The streamline upwinding method is usually employed to obtain the discretized form of Equation (3.73). The solution algorithm in the ALE technique is similar to the procedure used for a fixed VOF method. In this technique, however, the solution found at the end of the nth time step, based on mesh number n, is used as the initial condition in a new mesh (i.e. mesh number n + 1). In order to minimize the error introduced by this approximation the difference between the mesh configurations at successive computations should be as small as possible. Therefore the time increment should be small. In general, adaptive or re-raeshing algorithms are employed to construct the required finite element mesh in successive steps of an ALE procedure (Donea, 1992). In some instances it is possible to generate the finite element mesh required in each step of the computation in advance, and store them in a file accessible to the computer program. This can significantly reduce the CPU time required for the simulation (Nassehi and Ghoreishy, 1998). An example in which this approach is used is given in Chapter 5. [c.103]

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). [c.649]

The nght side of the curve tends to slope in an orderly manner and then falls off quite rapidly. If taken far enough, the compressor begins to choke or experience the effect of stonewall. If the internal Mach numbers are near 1 and/or the incidence angle on the inlet vane becomes high enough to reduce the entrance flow area and force the Mach number high enough, the compressor will choke. At this point, no more flow will pass through the compressor. The effect is much greater on high molecular weight gas, particularly at a low temperature and with the k value on the low side. The problem is that the compressor reaches the stonewall limit in flow before the designer had intended. If compressors are rerated, this elTeci must be kept in mind, particularly when the new conditions are for a low er [c.186]

All of the tests were with code conditions except for CO2 where the Mach number variance was more than plus 5%. The results are shown in Figure 10-4. It was concluded that the R12 test provided the more nearb/ [c.427]

Oxidation of polypropylene (PP) increased about 30% when the treatment time was increased from 1 min to 5 min at 60°C but was much lower than for hd-PE under similar conditions. The extent of oxidation for polystyrene (PS) at 60°C was much greater than for hd-PE. However, the N07/N0/ peaks were usually weaker than for the hydrocarbons. Numerous peaks with high mass numbers but low intensity were observed in the negative ion spectra, including tho.se characteristic ofCfiHsO and CsH70 (m/z — 93 and 119, respectively). In the positive spectra, the peak due to the protonated repeating unit (m/z = 105) was. split into two components the component at lowest mass number was assigned to C7H50" ". [c.309]

For the purpose of the cycle analyses (a) and (b), the following assumptions are made (i) cooling is of the open type, with a known air flow fraction (i//) first cooling a blade row and then mixing with the mainstream and (ii) complete mixing takes place, under adiabatic conditions, at constant static pressure and low Mach number (and therefore constant stagnation pressure). Before moving on to more realistic cycle calculations (but with the cooling air quantity (i//) assumed to be known), we consider the irreversibilities in the turbine cooling process, showing how changes in stagnation pressure and temperature (and entropy) are related to tjj. These changes are then used in cycle calculations for which ip is again sf>ecified, but real gas effects and stagnation pressure losses are included. [c.48]

The North American P-51 Mustang, designed at the outset of World War II, was the first production aircraft to employ a laminar flow airfoil. Flowever, laminar flow is a sensitive phenomenon it readily gets unstable and tries to change to turbulent flow. For example, the slightest roughness of the airfoil surface caused by such real-life effects as protruding rivets, imperfections in machining, and bug spots can cause a premature transition to turbulent flow in advance of the design condition. Therefore, most laminar flow airfoils used on production aircraft do not yield the extensive regions of laminar flow that are obtained in controlled laboratory tests using airfoil models with highly polished, smooth surfaces. From this point of view, the early laminar flow airfoils were not successful. However, they were successful from an entirely different point of view namely, they were found to have excellent high-speed properties, postponing to a higher flight Mach number the large drag rise due to shock waves and flow separation encountered near Mach 1. As a result, the early laminar flow airfoils were extensively used on jet-propelled airplanes during the 1950s and 1960s and are still employed today on some modem high-speed aircraft. [c.10]

A number of independent tiajectories, with up to 10 spawns each, were run to study the dynamics after excitation, with the initial conditions taken from the Wigner distribution. The results shows that initial motion is along the torsional motion to form the Dm twisted conformation. After a slight lag of 50-250 fs, this structm e starts to distort by pyramidalization of one of the ethylene groups. Crucially for the system dynamics, this leads to a conical intersection between Si and So- At this point, the system relaxes to the ground-state, but with an efficiency much less than 100% per pass of the intersection region. Interestingly, the character of the wave function at this point indicates that in fact the molecule is in the Z state, which in the distorted structure lies lower than the V. A study of the ethylene PES using more sophisticated quantum chemical methods [248] supports the observations from the dynamics that the relaxation mechanism for this system is not from the twisted structure as conventionally thought. [c.309]

For simulations of the motions of the atomic constituents of these molecules to be meaningful, the molecules must be placed in a natural environment, such as in a water bath or inside a membrane wall this increases the total number of atoms in the simulation by a significant factor (typically between 2 and 10). Even a large water bath by these standards is still extremely tiny, being only a few water molecules deep. Such simulations are adequate in some cases, but many properties of interest are distorted by surface effects and orientational correlations imposed by the small water bath and the finite system boundary. Periodic Boundary Conditions (PBC) have long been used to overcome the effects of a tiny simulation region by replicating the original simulation region a finite or infinite number of times in all directions (Fig. 1), the system s boundary is pushed out much further to infinity in the case of infinite PBCs. Particles in the replicated cell simply mimic the motions of the particles in the original unit cell each particle in the original cell feels the force induced by all other particles and all periodic images of all particles (including itself). [c.460]

Regardless of which approach is realized, during the development of an automatic JD structure generator several general problems have to be addressed. One major problem is the difference in conformational behavior of the cyclic and the acyclic portions of a molecule. Therefore, most 3D model builders treat rings and chains separately. Because of the ring closure condition, the number of degrees of freedom is rather restricted for ring systems compared with the opcn-chaiii portions. This geometrical constraint has to be taken into account in the 3D structure generation process. A method frequently applied to tackle this problem is to define allowed ring geometries (ring templates). These templates ensure a precise ring closure and can be chosen so that they represent a low-energy conformation for each ring size (e.g., the chair form of cyclohexane). A quite different situation is encountered for chain structures and substructures, The number of degrees of freedom, and thus the number of possible conformations, dramatically increase with the number of rotatable bonds. But which of all these conformations is the preferred one One approach is to stretch the main chains as much as po.ssiblc by setting the torsion angles to tram conhguration.s, unlc.ss a cis double bond is specified (principle of the longest pathways, i.e., stretching the main chains as long as possible see Figure 2-9.5). This method also effectively minimizes nonbonding interactions. Finally, the complete 3D model, i.e.. after the cyclic and acyclic portions have been reassembled, has to be checked for stcric crowding or atom overlap, and a mechanism should be implemented to eliminate such situations. [c.98]

As described in Chapter 1, mathematical models that represent polymer flow systems are, in general, based on non-linear partial differential equations and cannot be solved by analytical techniques. Therefore, in general, these equations are solved using numerical methods. Numerical solutions of the differential equations arising in engineering problems are usually based on finite difference, finite element, boundary element or finite volume schemes. Other numerical techniques such as the spectral expansions or newly emerged mesh independent methods may also be used to solve governing equations of specific types of engineering problems. Numerous examples of the successful application of these methods in the computer modelling of realistic field problems can be found in the literature. All of these methods have strengths and weaknesses and a number of factors should be considered before deciding in favour of the application of a particular method to the modelling of a process. The most important factors in this respect, are type of the governing equations of the process, geometry of the process domain, nature of the boundary conditions, required accuracy of the calculations and computational cost. [c.17]

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied [c.33]

We know from the section on molecular speads in Chapter 1 and Computer Project 3-2 that particles distribute themselves over an energy level spectrum in a very definite way, governed by the Boltzmann equation, Eq. (3-39), N = in the gravitational field. Equation (3-39) can be slightly modified by noting that mgh is the potential energy of an object of mass m in the potential field. If we use V to designate the potential energy not of gravity, but of twisting about the dihedral angle in n-butane, and if we use N to denote the number of n-butane molecules in the gauche condition relative to Nq molecules as the anti conformer. [c.126]

Mass-transfer coefficients are strongly affected by the degree of mobiUty of the drop surface. When the surface is free of adsorbed molecules it can move in response to surface shear stress, and the drops tend to circulate as they move through the continuous phase. However, even a trace of surface-active material can cause the drop surface to resist shear and the drop circulation is suppressed, resulting in greatly reduced mass transfer (43,44). Table 1 Hsts some of the proposed equations for mass transfer (expressed as SB) under various conditions. Nearly a threefold variation in dispersed-phase mass transfer exists between circulating and noncirculating drops. For the continuous phase the effect of circulation is greatest at high Reynolds number. For a more detailed assessment the specialized reviews (11,40,42) are recommended. [c.63]

See pages that mention the term

**Mach number conditions**:

**[c.649] [c.524] [c.127] [c.484] [c.666] [c.812] [c.1569] [c.502] [c.490] [c.352] [c.384] [c.518] [c.271] [c.553] [c.543] [c.130] [c.439] [c.68]**

Pressure safety design practices for refinery and chemical operations (1998) -- [ c.340 , c.346 , c.363 ]