The interrelation between void fraction fluctuations and flow patterns in two-phase flow

Transient and statistical measurement techniques for two-phase flows: A critical review

Fluidized-bed incineration of waste materials

Because the mathemat ica l models r equ i red for theore t ica l analyses of the p rob lem of two-phase flow a re quite complicated, the more successful approaches have been empir ica l and s e m i e m p i r i c a l . The major i ty of theore t ica l analyses [e.g., Harvey and Foust(41)] have assumed that the phases a r e mixed sufficiently to be cons idered as a homogeneous fluid. The work of Linning(66) is an example of a s e m i e m p i r i c a l approach; Linning s e t u p "one-dimensional" models for froth, s trat if ied, andannular flow configurations, determining unknown p a r a m e t e r s exper imental ly . Lockhar t and Martinelli(71) p resen ted a modera te ly successful cor re la t ion for the two-component problem. Mart inel l i and Nelson( ' ^ adapted the twocomponent cor re la t ion of Lockhar t and Martinelli(71) to s ingle-component sys tems by means of a simple cor rec t ion to account for changes in the axial component of momentum. The potential advantage of this approach over that of Harvey and Foust is the re la t ive simplici ty of the computations. However, Mart inel l i and Nelson did not p o s s e s s sufficient exper imenta l data to verify their approach. One of the most recent works on the predict ion of p r e s s u r e drop in two-phase , s ingle-component fluid flow is that of Isbin et al.(48) They conducted extensive exper imenta l work with s t eam-wate r mix tures at qual i t ies ranging from 3 to 98 per cent and at p r e s s u r e s ranging from 25 to 1415 psia . They at tempted to co r re l a t e their data by use of the Mart inel l i cor re la t ion , but found se r ious f low-rate and p r e s s u r e effects. The use of a homogeneous fr ict ion-factor model also proved unsuccessful . Therefore , they co r re l a t ed their data in a r e s t r i c t i ve manner which took into account the f low-rate and p r e s s u r e dependencies. In spite of the la rge amount of l i t e r a tu re in this a r e a , the information is still inadequate for obtaining accura te and re l iable design p rocedures for two-phase , s ingle-component flow sys t ems . 2.3. P a s t Work on Cr i t ica l Flow Much more is known about c r i t i ca l flow of a s ingle-phase fluid than is known about the two-phase c r i t i ca l flow of fluids. Many text books, such as that of HalH^O) a n d that of Shapiro,(89) a r e available which give the theory of s ingle-phase flow. Most of the r e s e a r c h which has been done in the genera l r e a l m of two-phase flow has concerned ei ther two-phase , two-component sys tems or two-phase , s ingle-component sys tems very close to sa turat ion condit ions. Most of the work involving the f i r s t has been done in the UnitedStates whereas Br i t i sh inves t igators have taken the initiative with the l a t t e r , by studying the behavior of sa tura ted water or mix tures of liquid water and s team resul t ing from some kind of an expansion or flashing p r o c e s s . The field being of such a complexity, it was not surpr i s ing to find a var ie ty of possible simplifying assumptions being made by different inves t iga to r s in an at tempt to bring theory close to fact. To date, however , no single design method has yet been proposed that will prove sat isfactory, except for a few limiting cases . The f i rs t r ea l a t tempts at a ser ious study of two-phase flow were probably those of Sauvage(85) i n 1892. According to Isbin,(46) Rateau(80) in 1902 showed the exis tence of c r i t i ca l flow in the flow of boiling water through nozzles . He obtained this c r i t i ca l condition by dropping the back p r e s s u r e until the d ischarge reached a maximum. He also developed a method of calculating the quantity of sa tura ted water d ischarged through a nozzle based upon isent ropic expansion. Mellanby and K e r r ( ' 5 ) in 1922 studied the flow of wet s t eam through nozzles . All four nozzles used were of the simple convergent or convergent para l le l type. Two of the nozzles were used in conjunction with a sea rch tube so that the t e s t s included p r e s s u r e m e a s u r e m e n t s as well as flow determinat ions . Only flow tes t s were c a r r i e d out on the other two, as these were not fitted with a sea rch tube. In all c a s e s , flow determinat ions were made with varying initial superheats at a supply p r e s sure of about 75 psia . The flow curves that these inves t igators have p r e sented for these four nozzles showed cer ta in var ia t ions between themselves but they all agreed on the two points: (1) that the flow, at and near the initially dry s ta te , was excess ive when compared with the theore t ica l as obtained on the assumption of stable expansion, and (2) that the form of the flow curve over a smal l range of superheat beyond the initially dry condition was not in agreement with the theore t ica l assumption of complete super saturat ion on any rat ional bas i s of expansion l o s s e s . Equations were developed in o rder to es t imate the "fractional revers ion" (fraction liquid actually p resen t / f r ac t ion liquid with no super saturat ion) existing in the nozzles . The fractional r eve r s ion was found to be l e s s for the nozzle with cent ra l search tube than for the ful l-bore jet. The difference seems r a the r unaccountable. F r o m their calcula t ions , it was noticed that the re was no indication of r eve r s ion before a value of roughly 1 \ per cent equivalent wetness was reached. The work of Stanton(94) i n 1926 gave valuable insight into the highspeed flow of a i r through sharp-edge or i f ices , convergent nozz les , and convergent-divergent nozzles . This invest igator obtained both axial and radia l p r e s s u r e profi les by using both search and Pi tot tubes . The most important conclusions derived in this work a re as follows: (1) In each of the three cha rac t e r i s t i c types of or if ices which may be used for the d i s charge of gases from a vesse l at constant p r e s s u r e into a r ece ive r at a p r e s s u r e appreciably below the c r i t i ca l value (0.527 t imes the u p s t r e a m stagnation p r e s s u r e ) , the a r ea of the je t diminishes to a minimum value, at which the velocity is that of sound under the conditions exist ing, and then i n c r e a s e s . This minimum section in the case of a free jet is not constant in a r e a or position re la t ive to the plane or throat of the or i f ice , but depends on the total ra t io of expansion. (2) In a jet in which the expansion takes place within solid boundar ies , i .e . , a diverging nozzle , the minimum section may for all p rac t ica l purposes be regarded as coincident with the throat of the nozzle for all ra t ios of expansion. (3) The flow of the fluid up to the minimum section is adiabatic in cha rac t e r . Goodenoughw^) i n 1927 said the fact that the speed of the water drops is only a small fraction of the speed of the s team has a decided effect on the discharge of wet s team, for the total friction is compr ised of not only the interact ion between the fluid and wal l s , but also of the internal interact ion between s team and water pa r t i c l e s . Goodenough further showed by calculation that super saturat ion would give a net i nc rease in isentropic flow for a given p r e s s u r e drop. He also pointed out that the surface energy of the droplets formed in such flows could be quite l a rge . Another compli cation is that any entrained drops (usually l a rge r than those formed by condensation) probably do not cool fast enough during the expansion to maintain the rmal equi l ibr ium with the s team. He points out that all the above could occur simultaneously in a flow p r o c e s s . Kit tredge and Dougherty(58) i n 1934 p resen ted an express ion for the calculation of c r i t ica l d ischarge capacity for s t eam t raps based on the initial and d ischarge p r e s s u r e s , and the specific volume of the mixture evaluated at the d ischarge p r e s s u r e . Their calculated values p resen ted in graphical form a re said to be 100 to 200 per cent g r e a t e r than exper imenta l values through a nozzle . In 1934, Yellott(105) investigated drop size and super saturat ion by studying the flow of l o w p r e s s u r e s team through nozzles s imi la r to those used in tu rb ines . This invest igator exper imental ly verif ied the existence of super sa turat ion with the aid of light r a y s , applications of the laws of opt ics , and a sea rch tube for nozz les . He found that the condensation occu r r ed between the 3 and 4 per cent mois tu re l ines on a Mollier d iagram if an isent ropic expansion is assumed. Rettaliatta '^-U in 1936 extended Yel lot t ' s work and intended p r i mar i ly to de termine the effect of wall roughness on the flow of s team in nozzles . It was found that wall roughness , causing a re ta rda t ion of s team flow, made the point of initial condensation occur at a higher p r e s s u r e and far ther downst ream than in the smooth-walled nozzle. This caused the Wilson line to occur at the 3.2 per cent mois tu re line on the Mollier diag r a m for the rough-walled nozzle , instead of at the 3.7 per cent mois tu re line as was found for the smooth nozzle. Ret tal ia t ta c la imed that this was the resu l t of the inc reased time of expansion in the case of the rough nozzle. In 1937, urged by a need for more information on c r i t i ca l flow for the design of cascading drain p ipes , Bottomley.i^O) experimenting with flow of boiling water through or i f ices , found that his actual flows based on exper imenta l data were 5 t imes g rea t e r than the predic ted values based on computation by the s ingle-phase equi l ibr ium theory. His explanation is that the effects of surface tensions lower the p r e s s u r e at which the propagation takes place. Because of surface tension, the condition of flow at the throat is that of unstable equilibrium. Bottomley further cites one experi

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Contribution to the theory of two-phase, one-component critical flow

Diagnostic procedures for establishing the quality of fluidization of gas-solid systems

In contrast to the single-phase flow, the gas-liquid two-phase flow is generally accompanied by violent pressure fluctuations. If the fluctuation is found to follow a certain law, the law may be useful in measuring the component flow in the two-phase mixture. From this view point, the pressure fluctuation was analyzed. This paper is the first report on the result of this analysis. A JIS orifice was fitted at the outlet of a vertical 1 inch bore pipe through which the airwater mixture flowed upward. The pressure at a point immediately before the orifice was recorded and analyzed. It was found that the pressure was either larger or smaller than the time-average pressure, and never stayed at the average amount. Therefore the time rate during which the pressure was larger than the average was definitely measurable. This quantity was named the liquid-phase time ratio, and its properties were examined. If the flow rate of each component of the gas-liquid mixture was given, the new quantity was found to have a definite amount.

Measurement of the Component Flows in a Vertical Two-Phase Flow by Making Use of the Pressure Fluctuation : Part 1,Proposal of a Characteristic Number

For the two-phase slug flow in the vertical tube, a simple flow model was proposed, by means of which the quantities defined in the previous report were theoretically correlated. A series of experiments was carried out, and it was proved that the actual slug flow could be fundamentally represented by the proposed flow model. Also the two-phase discharge coefficient of the orifice was defined and experimentally correlated with the component volume flow. It was found that the component flows could be estimated by measuring the average pressure drop across the orifice and the time ratio or the void ratio.

Measurement of the Component Flows in a Vertical Two-Phase Flow by Making Use of the Pressure Fluctuation : Part 2, The Flow Model for the Slug-Flow and Its Application

It is ordinarily assumed that the superheater and the reheater in boilers, unlike the evaporating section, do not generate pressure by absorbing heat. In this paper it is proved that the boiler pressure increases or decreases by manipulations that tend to increase or decrease the total volume of contained water in evaporators as well as in superheaters and reheaters. A simple theoretical reasoning leads us to conclude that the transfer function from the heat absorption to the steam pressure is mainly affected by the fluid-volume increase in the section devided by the outgoing (and not by the in-coming) fluid volume. Thus the pressure-generating effect in the superheater and the reheater in modern high-pressure boilers is nearly as large as, and sometimes even greater than, the effect in the evaporator. Similar investigation on the feedwater indicates that the steam pressure in supercritical boilers can better be controlled by manipulating the combustion than by manipulating the feedwater flow.

The Pressure-Generating Effect of Heat Absorption and Feedwater Flow in Boilers

The frequency distribution of the heat-flow intensity on the furnace walls radiated by homogenous gases which completely fill the furnace does not coincide with the distribution in the actual furnaces as tested by the ASME Committee. In an ideal furnace with a point heat source at its center, however, the frequency distribution is very similar to that of the intensity of heat-absorption in an actual furnace, provided radiation from the point heat source and radiation from the homogenous gas are combined properly. Since the distribution in a burner-fired furnace is not affected by the form of furnace or operating conditions, this fact may well be utilized in deriving an improved method of calculating heat-absorption in boiler-furnaces. Effective thickness of the flame in boiler furnaces as calculated by the Hottel method gives larger value than the rigorously calculated thickness. This is especially the case in a large modern furnace or with the luminous flame or powdered-coal flame. In this paper, the coefficients which give correct beam length are presented graphically.

Seikan Ishigai

Papers

Measurement of the Component Flows in a Vertical Two-Phase Flow by Making Use of the Pressure Fluctuation : Part 1,Proposal of a Characteristic Number

Measurement of the Component Flows in a Vertical Two-Phase Flow by Making Use of the Pressure Fluctuation : Part 2, The Flow Model for the Slug-Flow and Its Application

The Pressure-Generating Effect of Heat Absorption and Feedwater Flow in Boilers

Distribution of the Intensity of Heat-Absorption of Water-Walls in Burner-Fired Boiler-Furnaces

On the Flashing Flow of Saturated Water Through Horizontal Pipes