Mach number effects

A simple but effective technique for calculating the loss in an axial-flow turbine has been developed. In the loss computation, the blade geometry, the spacing between the blades, the aspect ratio, the thickness ratio, and the effect of the Reynolds number are taken into account. However, those factors not taken into account are the stagger angle, the trailing edge thickness, and the effects of Mach number. Neglecting Mach number effects causes a problem in the highly loaded stages. The optimum solidity (cr = c/s) of the blades is computed from  [c.365]

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]

One goal of catalyst designers is to constmct bench-scale reactors that allow determination of performance data truly indicative of performance in a full-scale commercial reactor. This has been accompHshed in a number of areas, but in general, larger pilot-scale reactors are preferred because they can be more fully instmmented and can provide better engineering data for ultimate scale-up. In reactor selection thought must be given to parameters such as space velocity, linear velocity, and the number of catalyst bodies per reactor diameter in order to properly model heat- and mass-transfer effects.  [c.197]

The scatteriag of x-rays (6,37,42) gives information on the average distances between the carbon atoms ia coal and iasight iato the bonding between these atoms. Because x-ray scatteriag depends on the number of protons ia the nucleus, carbon is much more effective ia scatteriag x-rays than hydrogen (see X-RAY technology). The ultraviolet and visible spectra (6) of coal and various solvent extracts show decreasiag absorption with increa sing wavelength and lack features to aid ia interpreting stmcture except for one peak around 270 nm, which is beheved to result from superposition of effects from many similar species. In studies of specific features, comparisons are usually made between coal or coal-derived samples, and pure, usually aromatic, compounds indicating probable presence of particular stmctures or functional groups. Similar statements can be made concerning reflectance and refractive index (3,4). The derived optical anisotropy is especially evident in coals having carbon contents that exceed 80—85 wt %. Measurements perpendicular and parallel to the bedding plane give different results for optical and some other characteristics (see Spectroscopy).  [c.220]

Factors that are important for the limitation of protected areas are the pipe network structure, degree of mesh, number of service pipes, type of pipe connections, quality of the pipe coating and availability of protection current as well as stray current effects. A protected area in a distribution network is shown in Fig. 10-11 with separate parts of the network (NT I to NT IV). Previous experience has shown that protected areas of 1 to 2 km with lengths of pipeline from 10 to 20 km are advantageous [30],  [c.285]

Free-vortex prewhirl. This type is represented by r Ve = constant with respect to the inducer inlet radius. This prewhirl distribution is shown in Figure 6-13. Vg is at a minimum at the inducer inlet shroud radius. Therefore, it is not effective in decreasing the relative Mach number in this manner.  [c.231]

In an ideal Bose gas, at a certain transition temperature a remarkable effect occurs a macroscopic fraction of the total number of particles condenses into the lowest-energy single-particle state. This effect, which occurs when the Bose particles have non-zero mass, is called Bose-Einstein condensation, and the key to its understanding is the chemical potential. For an ideal gas of photons or phonons, which have zero mass, this effect does not occur. This is because their total number is arbitrary and the chemical potential is effectively zero for tire photon or phonon gas.  [c.433]

Figures 10.1-7 and 10.1-8 differ because the toxicity of the compounds of Figure 10.1-7 is caused solely by their tendency to move into biological membranes and is often referred to as the baseline toxicity - a property that every compound has. However, in addition to that, many compounds can interact with more specific targets. So it is necessary to have QSAR-equations with additional terms that account for electronic and steric effects. However, these are much harder to model and most models are based on the common chemical class of compounds. As a result, we face the problem today that there is a huge number of QSAR equations of a very local nature. The methods applied range from quite simple extension of Eq. (15) to CoMFA models. The descriptors also cover a wide range of types, with global whole-molecule descriptors being used the most often [34]. A major problem is the choice of the appropriate QSAR for the prediction of a new compounds, and there is a great danger of applying inappropriate QSARs. One suggestion of a way to resolve this problem is to establish models that are based on a common MOA Figures 10.1-7 and 10.1-8 differ because the toxicity of the compounds of Figure 10.1-7 is caused solely by their tendency to move into biological membranes and is often referred to as the baseline toxicity - a property that every compound has. However, in addition to that, many compounds can interact with more specific targets. So it is necessary to have QSAR-equations with additional terms that account for electronic and steric effects. However, these are much harder to model and most models are based on the common chemical class of compounds. As a result, we face the problem today that there is a huge number of QSAR equations of a very local nature. The methods applied range from quite simple extension of Eq. (15) to CoMFA models. The descriptors also cover a wide range of types, with global whole-molecule descriptors being used the most often [34]. A major problem is the choice of the appropriate QSAR for the prediction of a new compounds, and there is a great danger of applying inappropriate QSARs. One suggestion of a way to resolve this problem is to establish models that are based on a common MOA
Let us now consider the role of pressure gradients in catalyst pellets. The literature contains numerous statements to the effect that reactions involving a change in number of molecules will be accompanied by pressure gradients within a catalyst pellet, the pressure increasing towards the center of the pellet when the number of molecules increases in the reaction. There are also discussions of the importance of this pressure gradient, both from the point of view of its possible influence on the flux vectors and the effectiveness factor, and also regarding its possible mechanical effect on the structure of the pellet. As there appear to be many misunderstandings and much confusion, It Is worthwhile spending a little time examining these questions.  [c.128]

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 much less basis set dependent method is to analyze the total electron density. This is called the atoms in molecules (AIM) method. It is designed to examine the small effects due to bonding in the primarily featureless electron density. This is done by examining the gradient and Laplacian of electron density. AIM analysis incorporates a number of graphic analysis techniques as well as population analysis. The population analysis will be discussed here and the graphic techniques in the next chapter.  [c.101]

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]

The second class, indeterminate or random errors, is brought about by the effects of uncontrolled variables. Truly random errors are as likely to cause high as low results, and a small random error is much more probable than a large one. By making the observation coarse enough, random errors would cease to exist. Every observation would give the same result, but the result would be less precise than the average of a number of finer observations with random scatter.  [c.192]

Sulphur in hydrogen sulphide and its derivatives is a much less effective simple electron pair donor and the other Group VI elements show this property to a very minor extent. However, compounds based on divalent sulphur (for example, dimethylsulphide (CH3)2S) are often found to be effective ligands in transition metal complexes. Unlike oxygen, the remaining elements can increase their covalency to a maximum of six by utilising the low energy d orbitals not available to oxygen, and 6— coordinate compounds (for example SFg) are known. However, as the atomic number and size of the atoms increase from oxygen to polonium, the elements become more electropositive, the hydrides less stable and the stabilities of the higher oxidation states decrease. Only polonium can really be said to show weakly metallic properties, although tellurium oxides are amphoteric.  [c.259]

Metal and Ceramic Membranes. Palladium and palladium alloy membranes can be used to separate hydrogen from other gases. Palladium membranes were studied extensively during the 1950s and 1960s, and a commercial plant to separate hydrogen from refinery off-gas was installed by Union Carbide (53). The plant used palladium—silver alloy membranes in the form of 25-p.m thick films. The plant was operated for some time, but a number of problems, including long-term membrane stability under the high temperature operating conditions, were encountered, and the plant was later replaced by pressure-swing adsorption systems. Small-scale palladium membrane systems, marketed byjohnson Matthey and Co., are still used to produce ultrapure hydrogen for specialized appHcations. These systems use palladium—silver alloy membranes, based on those originally developed (54). Membranes with much thinner effective palladium layers than were used in the Union Carbide installation can now be made. One technique is to form a composite membrane comprising a polymer substrate onto which is coated a thin layer of palladium or palladium alloy (55). The palladium layer can be appHed by vacuum methods, such as evaporation or sputtering. Coating thicknesses on the order of 100 nm or less can be achieved.  [c.69]

Control of Exposure Potentia.1. Exposure to toxic materials can be controlled by a number of methods, eg, substitution, removal, enclosure, and personal protection. The best method of protecting workers is by substituting a less toxic material for a more toxic substance having equal effectiveness, eg, the use of 1,1,1-trichloroethane for carbon tetrachloride, and toluene for ben2ene. Ventilation at the work location is much more effective in removing undesirable contaminants than general room ventilation (59). Suitable exhaust hoods or flexible ducts should be utili2ed to draw off contaminated air as near to the point of chemical release as is feasible. Some operations can be completely enclosed, eg, continuous processing in contrast to batch operation, where process vessels are opened occasionally. Personal protection, the last point of defense, sometimes is the only way in which a worker can be protected from exposure. Such protection includes a hard hat, face shield or goggles, apron, coat, pants, and boots or mbber shoes. Respiratory protection may be provided by a dust respirator, canister gas mask (if sufficient oxygen is always present), self-contained breathing equipment, or airline respirators (53). Recent OSHA requirements for breathing apparatus specify special fit-testing of masks and positive pressure face masks, so that any air contaminants present do not leak inward through gaps at the edges of the mask.  [c.96]

The theories discussed so far adequately account for agents consisting only of insoluble Hquids such as siUcone fluids used in the defoaming of crude oil. However, practical experience also shows that dispersed hydrophobic soflds can greatly enhance defoamer effectiveness in certain cases, particularly in aqueous foam systems. Materials such as hydrophobic siUca (13) or high melting-point hydrocarbon amides such as ethylenediamine distearamide are notably effective. A strong correlation between defoamer action and contact angle for siUcone-treated siUca in a hydrocarbon oil has been demonstrated (32). Most recent pubHcations on the mechanism of defoamers have concentrated on the role of the dispersed hydrophobic soflds. There are a number of contradictory older hypotheses for their mode of action that have been discounted (33) and replaced with the idea that dewetting of the hydrophobic siUca by the bubble film causes foam coUapse by the direct mechanical shock of the event (33,34). Such dewetting helps thin the film and promote instabiUty, and is particularly effective when sizes are such that the particle occupies both surfaces of the film. In this bridged situation, if the contact angle is large enough, a capillary pressure drop that pushes Hquid away from the particle is developed (34). This flow results in migration of the air-hquid-sohd interfaces towards each other until they meet and the film mptures as it pinches off the particle. This concept offers an explanation for observed particle size and shape effects (14,34,35). Note also that Hquid droplet antifoaming can be interpreted in terms of dewetting by the foam film rather than by the spreading mechanism (36), although Hquid particles have been found to be much less effective than soHd particles (35). A number of cinephotomicrographic studies are consistent with these dewetting ideas (37,38).  [c.466]

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number.  [c.648]

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 refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-  [c.181]

The excited states of a Rydberg series have an electron in an orbital of higher principal quantum number, n, in which it spends most of its time far from the molecular framework. The idea is that the electron then feels mainly a Coulomb field due to the positive ion remaining behind at the centre, so its behaviour is much like that of the electron in the hydrogen atom. The constant 8 is called the quantum defect and is a measure of the extent to which the electron interacts with the molecular framework. It has less influence on the energy levels as n gets larger, i.e. as the electron gets farther from the central ion. The size of 8 will also depend on the angrilar momentum of the electron. States of lower angrilar momentum have more probability of penetrating the charge cloud of the central ion and so may have larger values of 8. Actual energy levels of Rydberg atoms and molecules can be subject to theoretical calculations [27]. Sometimes the higher states have orbitals so large that other molecules may fall within their volume, causing interesting effects [28].  [c.1145]

Mesoscopic and continuum models do not attempt to describe large-scale phenomena starting from the smallest atomic length scale, but rather incorporate the local structure via a small number of effective parameters. Mesoscopic models lump a small number of atoms into an effective particle. These particles interact via coarse-grained interactions. By this coarse-graining procedure much of the atomistic detail is lost, and only those interactions pertinent to the phenomena on the mesoscopic lengdi scales are retained. Even if the interactions on the microscopic scale are extremely complex (e.g., hydrophobic interactions [3] in lipid water mixtures), they can often be captured by simple expressions on the mesoscopic lengdi scale. Coarsegrained models thus yield valuable insights into the structure on large length scales. For specific examples the effective interactions are derived by eliminating the degrees of freedom on the smallest (atomistic) lengdi scales, retaining only those on larger lengdi scales for some systems (e.g., polymer chains in the gas phase) this coarse-graining procedure has a fomial justification due to the self-similar structure on a large range of lengdi scales for other systems the mapping between the atomistic/microscopic level and the mesoscopic description is ratiier a concept than a practicable procedure. In this latter case, the application of mesoscopic models rests on the observation that different systems (e.g., diblock copolymers and lipid water mixtures) share a connnon behaviour on mesoscopic scales. Universal mesoscopic behaviour that does not depend on the details on the atomistic level in a qualitative way is the subject of mesoscopic models.  [c.2363]

In quantum wells, Heisenberg s uncertainty principle requires an increase in the carrier energy over tire equilibrium energy of the bulk semiconductor. The confined carriers are allowed only a few discrete states, witli energies inversely proportional to tire carrier s effective mass and tire square of tire well widtli. The incoryDoration of quantum wells into tire material has a number of subtle consequences. The VB in direct bulk semiconductors is degenerate at tire T point (see figure C2.16.5, resulting in two types of holes witli tire same energy, tire heavy holes and light holes. The effective mass of tire light hole is similar to that of tire electron, while tliat of tire heavy hole is typically ten times larger tlian tliat of tire electron. In quantum wells, tire degeneracy of tire two hole bands is lifted. The energy shift due to quantum well confinement is larger for tire light holes. This has important consequences for quantum well lasers and modulation-doped FETs.  [c.2894]

The splitting of the quantum propagator negatively effects the efficiency of the scheme especially if m/M is small, i.e., if the quantum oscillation are much faster than the classical motion and the number n of substeps is becoming inefficiently large.  [c.402]

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, 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]

In order to predict the overall chemical reaction rate In a catalyst pellet, it is necessary to be able to write down correct differential material balances, which can then be Integrated to give the required re action rate or effectiveness factor, There is, of course, an enormous literature on this subject, but surprisingly the great majority of this is confined to one or two rather unrealistic special cases. Much the largest number of papers use flux relations applicable only to binary mixtures, and may slip implicitly Into further constraints which limit the validity of their material balances to a simple isomerization A B. Nevertheless, the resulting differential eouatlons are often used to determine the concentration profile of one component In a multicomponent mixture. Certain papers formulate material balances which are correct for any reaction of the form A nB (where n is not necessarily unity), provided all pores are large compared with the mean free path lengths. Others formulate balances which are correct In multicomponent mixtures, but only when all pores are narrow compared with the mean free path lengths, so that Knudsen diffusion controls. In realistic situations, however, the reaction mixture is very rarely binary and the pore size distribution Is commonly either very broad or bimodal, with Knudsen diffusion controlling in the smallest pores and the larger pores of such a size that the diffusion mechanism lies in the intermediate range between the extremes of Knudsen and bulk diffusion control. When the distribution is strongly bimodal and the micropores are predominantly dead-ended, their Influence can be taken Into account simply by defining a modified reaction rate function relating the total reaction rate per unit pellet volume to the local composition in the macropore system. Using appropriate flux relations for the macropores, it should then be possible to predict the Influence of pellet dimensions and macropore structure on the overall reaction rate. However, to accomplish even  [c.110]

Obviously selection of the most efficient elements in conjunction with the most appropriate finite element scheme is of the outmost importance in any given analysis. However, satisfaction of the criteria set by these considerations cannot guarantee or even determine the overall accuracy, cost and general efficiency of the finite element simulations, which depend more than any other factor on the algorithm used to solve the global equations. To achieve a high level of accuracy in the simulation of realistic problems usually a refined mesh consisting of hrmdrcds or even thousands of elements is used. In comparison to time spent on the solution of the global set, the time required for evaluation and assembly of elemental stiffness equations is small. Therefore, as the number of equations in the global set grows larger by mesh refinement the computational time (and hence cost) becomes more and more dependent on the effectiveness and speed of the solver routine. The development of fast and accurate computational procedures for the solution of algebraic sets of equations has been an active area of research for many decades and a number of very efficient algorithms are now available.  [c.199]

The FMO theory states that a reaction between two compounds is controlled by the efficiency with which the molecular orbitals of the individual reaction partners interact. The interaction is most efficient for those orbitals that overlap best and are closest in energy. The FMO theory further assumes that the reactivity is completely determined by interactions of the electrons that are highest in energy of one of the reaction partners (i.e. those in the Highest Occupied Molecular Orbital, the HOMO) with the Lowest Unoccupied Molecular Orbital (LUMO) of the other partner. Applied to the Diels-Alder reactions, two modes of interaction are possible the reaction can be controlled by the interaction of the HOMO of the diene and the LUMO of the dienophile (normal electron demand), or by the interaction between the LUMO of the diene and the HOMO of the dienophile (inverse electron demand), as illustrated in Figure 1.1. In the former case, a reduction of the diene-HOMO dienopWle-LUMO energy gap can be realised by either raising the energy of the HOMO of the diene by introducing electron donating substituents or lowering the energy of the dienophile-LUMO by the introduction of electron withdrawing substituents. A glance at Figure 1.1 confirms that in the formation of two new c-bonds, orbital symmetry is conserved so that, according to Woodward and Hoffmann, the reaction is concerted. In other words, no intermediate is involved in pericyclic processes such as the Diels-Alder reaction ". This conclusion is consistent with a number of experimental observations (a) The cis or trans conformation of the dienophile is fully conserved in the configuration of the cycloadduct, which proves that there is no intermediate involved with a lifetime long enough to allow rotation around a C-C bond (b) The Hammett p-values, which can be considered as a measure of the development of charge in the activation process, are much smaller than those obtained for reactions known to proceed through charged intermediates, (c) Solvent effects on the Diels-Alder reaction are usually small or modest (see Section 1.2.3), excluding the  [c.4]

Aspinn possesses a number of properties that make it an often recommended drug It is an analgesic effective m relieving headache pain It is also an antiinflammatory agent providing some relief from the swelling associated with arthritis and minor injuries Aspinn IS an antipyretic compound that is it reduces fever How aspmn does all this was once a mystery but is now better understood and will be discussed m Section 26 6 Each year more than 40 million lb of aspirin is produced m the United States a rate equal to 300 tablets per year for every man woman and child  [c.1006]

See pages that mention the term Mach number effects : [c.1569]    [c.787]    [c.54]    [c.101]    [c.498]    [c.80]    [c.429]    [c.2564]    [c.371]    [c.26]    [c.468]    [c.521]    [c.643]    [c.1144]    [c.22]    [c.174]    [c.271]    [c.178]   
Turboexpanders and Process Applications (0) -- [ c.105 ]