# The simple approach

We concentrate here on open loop cooling in which compressor air mixes with the mainstream after cooling the blade row, the system most widely used in gas turbine plants (but note that a brief reference to closed loop. steam cooling in combined cycles is made later, in Chapter 7). For a gas turbine blade row, such as the stationary entry nozzle guide vane row where most of the cooling is required, the approach first described here (called the simple approach) involves the following [c.60]

In the simple approach, the change po due to Q (the first term in Eiq. (4.42)) is usually ignored for both streams. The change of po due to frictional effects in the mainstream flow is usually included in the basic polytropic efficiency (rjp) of the uncooled flow, so that [c.62]

In this preliminary work we have investigated composite objects with a simple geometry. In future work the proposed approach will be applied to more complicated objects, in particular glued structures. Since we for such objects expect to have a less distinct back wall echo, we have reason to believe that the preprocessing method that was used in this work has to be somewhat modified. [c.893]

The total interaction between two slabs of infinite extent and depth can be obtained by a summation over all atom-atom interactions if pairwise additivity of forces can be assumed. While definitely not exact for a condensed phase, this conventional approach is quite useful for many purposes [1,3]. This summation, expressed as an integral, has been done by de Boer [8] using the simple dispersion formula, Eq. VI-15, and following the nomenclature in Eq. VI-19 [c.232]

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. [c.618]

This method relies on the simple principle that the flow of ions into an electrolyte-filled micropipette as it nears a surface is dependent on the distance between the sample and the mouth of the pipette [211] (figure B 1.19.40). The probe height can then be used to maintain a constant current flow (of ions) into the micropipette, and the technique fiinctions as a non-contact imaging method. Alternatively, the height can be held constant and the measured ion current used to generate the image. This latter approach has, for example, been used to probe ion flows tlirough chaimels in membranes. The lateral resolution obtainable by this method depends on the diameter of the micropipette. Values of 200 nm have been reported. [c.1718]

Unfortunately, this simple approach is not plausible numerically. The integral, as presented, will not converge, even for short times. The problem is that even trajectories which are wild , i.e. highly fluctuating, contribute. [c.2314]

The examples of modelling discussed in section C2.5.2 and section C2.5.3 are meant to illustrate tlie ideas behind tlie tlieoretical and computational approaches to protein folding. It should be borne in mind tliat we have discussed only a very limited aspect of tlie rich field of protein folding. The computations described in section C2.5.3 can be carried out easily on a desktop computer. Such an exercise is, perhaps, tlie best of way of appreciating tlie simple approach to get at tlie principles tliat govern tlie folding of proteins. [c.2659]

The simplest approach to understanding the reduced melting point in nanocrystals relies on a simple thennodynamic model which considers the volume and surface as separate components. Wliether solid or melted, a nanocrystal surface contains atoms which are not bound to interior atoms. This raises the net free energy of the system because of the positive surface free energy, but the energetic cost of the surface is higher for a solid cluster than for a liquid cluster. Thus the free-energy difference between the two phases of a nanocrystal becomes smaller as the cluster size [c.2912]

The underlying principle of the PEOE method is that the electronic polarization within the tr-bond skeleton as measured by the inductive effect is attenuated with each intervening o -bond. The electronic polarization within /r-bond systems as measured by the resonance or mesomeric effect, on the other hand, extends across an entire nr-system without any attenuation. The simple model of an electron in a box expresses this fact. Thus, in calculating the charge distribution in conjugated i -systems an approach different from the PEOE method has to be taken. [c.332]

The basic approach to the problem of estimating properties can be written in a very simple form that states that a molecular property P can be expressed as a function of the molecular structure C (Eq. (1)). [c.487]

It was pointed out in Chapter 2 that the general theory of pressure driven flow in a capillary, throughout the intermediate range where mean free path length and tube diameter are comparable, has so far proved intractable. For just the same reasons we have no complete theory of thermal transpiration in a capillary to span the range of cube diameters between Knudsen streaming and Maxwell s calculation. However, it is possible to approach this problem through the dusty gas model, which once again demonstrates its power by predicting both thermal transpiration and thermal diffusion, throughout the Intermediate range of pore sizes, and for mixtures of any number of species rather than just a pure gas. Furthermore, as we shall see, the results reduce to equations (A.1.2) and (A.1.8) above in the simple limiting cases. A good account of this aspect of the dusty gas model has been given by Wong and Denny [68]. [c.182]

Having noted that each field of chemistry brings a unique perspective to the study of chemistry, we now ask a second deceptively simple question. What is the analytical perspective Many analytical chemists describe this perspective as an analytical approach to solving problems. Although there are probably as many descriptions of the analytical approach as there are analytical chemists, it is convenient for our purposes to treat it as a five-step process [c.5]

In developing this treatment for determining equilibrium constants, we have considered a relatively simple system in which the absorbance of HIn and Im were easily measured, and for which it is easy to determine the concentration of H3O+. In addition to acid-base reactions, the same approach can be applied to any reaction of the general form [c.409]

The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, X and Y, that are similar in both matrix and concentration of analyte. The results obtained by each analyst are plotted as a single point on a two-sample chart, using the result for one sample as the x-coordinate and the value for the other sample as the -coordinate. [c.688]

Micronutrients in Granular Fertilizers. In the production of granular fertilizers, it is relatively simple and effective to incorporate micronutrient materials as feeds in the granulation process. A problem with this method, however, is that granulation processes are most efficient and economical when operated continuously to produce large tonnages of the same or similar composition. Frequent changes in product composition or storage of a wide range of grades is simply uneconomical. These factors seriously limit the practice of prescription micronutrient formulation in granular fertilizer production processes. Granulation processes more often use the shotgun approach. As a result, some unneeded elements are provided with no benefit. [c.242]

Cost Calculation. The main elements determining production cost are identical for fine chemicals and commodities (see Economic evaluation), a breakdown of production cost is given in Table 2. In multipurpose plants, where different fine chemicals occupying the equipment to different extents are produced during the year, a fair allocation of costs is a more difficult task. The allocation of the product-related costs, such as raw material and utiHties, is relatively easy. It is much more difficult to allocate for capital cost, labor, and maintenance. A simplistic approach is to define a daily rent by dividing the total yearly fixed cost of the plant by the number of production days. But that approach penalizes the simple products using only part of the equipment. [c.440]

One of the earliest configurations studied was the simple magnetic mirror. A simple mirror system is depicted in Figure 1. Particles gyrating about the field lines move freely along these lines until they enter regions of increased field strength at either end of the device. Conservation of angular momentum considerations dictate that, as the particles approach the end regions, they gyrate mote energetically about the field lines and slow down in the direction of motion along the lines. Ultimately, their kinetic energy is completely converted into gyration energy, at which point the particles ate reflected from these mirror points and return to the central, weaker field region. Particles having motion exactly along the axis of the device ate not reflected and ate lost through the ends. Although ingenious attempts have been made to reduce end losses from mirror machines and to make them stable against magnetohydrodynamic (MHD) and other instabiUties, all single-cell mirror reactor designs have suffered from a high recirculating power fraction, ie, a lot of the output power has to be used to operate the reactor itself. In single-cell mirror machines these losses ate fundamentally too high. The machines ate referred to as too lossy, and the amount of injected power required to maintain the plasma, usually in the form of high energy neutral beams, has been too large to be practical. [c.151]

These methodologies have been reviewed (22). In both methods, synthesis involves assembly of protected peptide chains, deprotection, purification, and characterization. However, the soHd-phase method, pioneered by Merrifield, dominates the field of peptide chemistry (23). In SPPS, the C-terminal amino acid of the desired peptide is attached to a polymeric soHd support. The addition of amino acids (qv) requires a number of relatively simple steps that are easily automated. Therefore, SPPS contains a number of advantages compared to the solution approach, including fewer solubiUty problems, use of less specialized chemistry, potential for automation, and requirement of relatively less skilled operators (22). Additionally, intermediates are not isolated and purified, and therefore the steps can be carried out more rapidly. Moreover, the SPPS method has been shown to proceed without racemization, whereas in fragment synthesis there is always a potential for racemization. Solution synthesis provides peptides of relatively higher purity however, the addition of hplc methodologies allows for pure peptide products from SPPS as well. [c.200]

Here we first describe the simple approach, assuming that ip is known, and describe how /),) and To downstream of the cooled row are obtained (steps (a) and (b) above). We then briefly describe the YoungAVilcock approach which leads to the determination and summation of the component entropy increa.ses, again for a given ip. [c.60]

The simple approach described before involves approximations, particularly to obtain the stagnation pressure loss. The full determination of pf) m (7 o)5m from the various equations given above can lead to an approximation for the downstream entropy (.vsni). using the Gibbs relation applied between stagnation states. [c.64]

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. [c.485]

There has been considerable elaboration of the simple Girifalco and Good relationship, Eq. XII-22. As noted in Sections IV-2A and X-6B, the surface ftee energies that appear under the square root sign may be supposed to be expressible as a sum of dispersion, polar, and so on, components. This type of approach has been developed by Dann [70] and Kaelble [71] as well as by Schonhom and co-workers (see Ref. 72). Good (see Ref. 73) has preferred to introduce polar interactions into a detailed analysis of the meaning of in Eq. IV-7. While there is no doubt that polar interactions are important, these are orientation dependent and hence structure sensitive. [c.453]

Several other improvements of the inversion-recovery scheme employ advanced tools of modem NMR spectroscopy polarization transfer and two-dimensional spectroscopy (see fiirther reading). The basic design of selected pulse sequences is compared with the simple inversion-recovery scheme in figure Bl.13.5 taken from Kowalewski and Maler [24], where references to original papers can be found. The figure Bl.13.5(a), where thick rectangular boxes denote the 180° /-spin pulses and thin boxes the corresponding 90° pulses, is a representation of the inversion-recovery sequence with the continuous saturation of the protons. In figure B1.13.5(b), the inverting /-spin pulse is replaced by a series of pulses, separated by constant delays and applied at both the proton and the /-spm resonance frequencies, which creates a more strongly polarized initial /-spin state (the polarization transfer teclmique). In figure B1.13.5(c), a two-dimensional (2D) NMR teclmique is employed. This type of approach is particularly usefiil when the sample contains many heteromiclear IS spin pairs, with different /s and different. S s characterized by slightly different resonance frequencies (chemical shifts), resulting in crowded spectra. In a generic 2D experiment, the NMR signal is sampled as a fiinction of two time variables t is the miming tune during which the FID is acquired (different [c.1508]

This section summarizes the results of a study of internal hydration of protein molecules, based on a very simple approach, in which only the intermolecular energy of protein and ligand was considered, and also describes the Dowser tool that was developed as a result of that study [37]. Water molecules inside cavities in proteins constitute integral parts of the structure. In most of the filled cavities, the internal water molecules are held with two or more hydrogen bonds, while cavities without hydrogen bonding groups on the surface are empty. Due to experimental error and interpretative uncertainty of electron density maps, internal water positions cannot always be unequivocally assigned the problem is worse for structures determined at lower resolution. We have sought a quantitative measure of the hydrophilicity of the cavities by calculating the energy of introducing a water molecule into a cavity, using the known structure of the protein and standard molecular mechanics energies. In a survey of a number of proteins, it was found that a threshold value of the water-protein interaction energy at -12 kcal/mol distinguished hydrated from empty cavities. In one instance of two independent crystallographic determinations of the same structure [2, 24], we were able to conclude on the basis of these energies and additional crystallographic information (occupancy and B-factor) that in one structure many more buried water sites had been assigned than were, in fact, physically present. [c.136]

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the [c.137]

The CFTI method is highly efficient, has improved convergence properties and enables new ways of exploring energy landscapes of flexible molecules. The efficiency is due to the fact that calculation of the free energy gradient with respect to an arbitrary number of coordinates may be performed at essentially the same cost as a standard one-dimensional TI simulation under the same conditions [2]. This is because the most expensive terms to evaluate, dU/d k, may be expressed in terms of simple algebraic transformations of the Cartesian gradient dU/dqj, which is known at each step of a simulation [2, 8]. A single simulation yields derivatives of free energy with respect to all conformational degrees of interest, yielding a complete local characterization of conformational space, not just the derivative along a one-dimensional reaction path [2, 8]. This enables the determination of stability of structures with respect to perturbations, location of minima on the free energy surface, and finding minimum free energy paths connecting different states. The accelerated convergence may be achieved by selecting all soft degrees of freedom as the fixed coordinates. In the case of peptides these would be the backbone 4>, Ip, and some of the sidechain dihedrals [8, 9, 10]. The sampling of the restricted conformational space of remaining hard degrees of freedom and solvent is very fast - simulations of 20-50 ps were sufficient to obtain precise gradient values in the studied cases. Simulations of similar length are sometimes used in the standard approach to free energy profiles, where only the reaction coordinate is constrained. However in these methods, because of the size of the available conformational space, the convergence of thermodynamic averages is often assumed rather than actually achieved. [c.166]

An enhancement of the simple substructure approach is the Fragment Reduced to an Environment that is Limited (FREL) method introduced by Dubois et al. [7] With the FREL method several centers of the molecule are described, including their chemical environment. By taking the elements H, C, N, O, and halogens into account and combining all bond types (single, double, triple, aromatic), the authors found descriptors for 43 different FREL centers that can be used to characterize a molecule. [c.516]

A simple example is the formation of the hydrogen molecule from two hydrogen atoms. Here the original atomic energy levels are degenerate (they have eipial energy), but as the two atoms approach each other, they interact to form tw u n oiuiegcn crate molecular orbitals, the lowest of which is doubly occupied. [c.49]

L. iitortunately, this simple approach does not work well, but Becke has proposed a strategy which does seem to have much promise [Becke 1993a, b]. In his approach the exchange-correlation energy Exc is written in the following form [c.155]

If T is large, then the coupling will be weak. If t is small, the coupling will be strong a when the coupling parameter equals the time step (t = St) then the algorithm is equivak to the simple velocity scaling method. A coupling constant of approximately 0,4 ps has be suggested as an appropriate value to use when the time step is 1 fs, giving St/r 0.0025. T advantage of this approach is that it does permit the system to fluctuate about the desir temperature. [c.399]

US model can be combined with the Monte Carlo simulation approach to calculate a r range of properties them is available from the simple matrix multiplication method. 2 RIS Monte Carlo method the statistical weight matrices are used to generate chain irmadons with a probability distribution that is implied in their statistical weights. [c.446]

There are many ways in which the structure for input to the next iteration of the search cai be selected. A simple approach is to take the structure obtained from the previous step. Ai alternative is to select randomly a structure from those generated previously, weighting th choice towards those structures that have been selected the least (a uniform usage protocol). J third method is to use the lowest-energy structure found so far, or to bias the selectioi towards the lowest-energy structures. The Metropolis Monte Carlo scheme is often usei to make the choice. Each newly generated structure (after energy minimisation) is acceptei as the starting point for the next iteration if it is lower in energy than the previous structur or if the Boltzmarm factor of the energy difference, exp[— is large [c.483]

ITiis chapter does not introduce new chemical reactions. On the contrary, mainly elementary reactions are employed. The attempt is made here to provide an introduction into the planning of syntheses of simple "target molecules" based upon the synthon approach ofE.J. Corey (1967A, 1971) and the knowledge of the market of "fine chemicals". [c.171]

The solution of equation 16 is a decreasing, simple exponential where = k ([A ] + [P ]) + k. The perturbation approach generates small deviations in concentrations that permit use of the linearized differential equation and is another instance of pseudo-first-order behavior. Measurements over a range of [A ] + [T ] allow the kineticist to plot against that quantity and determine / ftom the slope and from the intercept. [c.510]

See pages that mention the term

**The simple approach**:

**[c.61] [c.1265] [c.1509] [c.53] [c.389] [c.389] [c.381] [c.498] [c.13] [c.256] [c.370] [c.430] [c.612] [c.45] [c.311]**

See chapters in:

** Advanced gas turbine cycles
-> The simple approach
**