JOURNAL O F RESEAR CH 01 the Notionol Bureou of Standards - C. Engineering ond Instrumentation Vol. 72C, No.1 , Jonuary- Morch 1968 An Adiabatic Saturation Psychrometer
Lewis Greenspan and Arnold Wexler
Institute for Basic Standards, National Bureau of StandaFds, Washington, D.C. 20234
(November 17, 1967)
An adiabatic satu ration psychromet e r for measuring the humidity of gases, as well as the vapor content of va por-gas mlXtures, IS descrIbed: The. In strument behaves in accordance with predictions d e du ~ e d solely fro m thermodyna mIc consIderatIO ns. With water-air, water-hydrogen, carbon tetra c hl o ~ld e - h y d roge n , carbon tetrachlonde-oxygen and tolue ne-air syste ms, at room te mperature, atmos pherI c pressure, and ~a s fl ow rates ?f 1.3 to 5.2 liters pe r minute, measured wet-bulb te mperatures agree WIth calc ul ated thermod yna mIc ~ e t-bul b tempera tures" to within the accuracy of the measure ments and the uncertamtles I~ the publIshed the rmodynamic data used in the computations. For the wate r-aIr syste m, the systema tI c and ra ndom errors due to these sources are estima ted at 0 027 deg C and 0.019 deg C r e~ p ec tiv e l y. The agreement between the cal cul ated and measured wet-bulb te mpera ture. IS 0.029 deg C, whle h a t a dry-bulb temperature of 25 °C and an ambient pressure of 1 bar is e qUlv ~ l e nt to a n uncertalllty In relative humidity which varies from 1/8 to 1/4 percent. The time con ~ tant IS a functIOn of the gas fl ow rate; at fl ow rates of 3_ 75 to 5_2 liters per minute, the time constant IS of the order of 3/4 mmute.
Key Words: Adia bati c satu ration, gas mixtures, humidity, hyg rome te r, mixing ratio, moist gas, psychrometer, psychrometnc factor, saturation, thermod yna mic wet-bulb te mper a ture, vapor conte nt, wet-bulb.
1. Introduction yield results that are in nominal agreement with empirical facts for water vapor-air mixtures_ When The psychrometer is one of the oldest and most these formulas are applied to other vapor-gas mix common instruments for meas uring the humidity of tures, they fail to predict the correct vapor conte nt. moist air. In its elemental form it consists of two The wet-bulb thermometer of a psyc hrometer in a thermometers; the bulb of one is cov ered with a wic k steady-state condition experiences simultaneous heat and is moistened; the bulb of the other is left bare and and mass transfer. Although theories based on heat dry_ Evaporation of water from the moistened wick and mass transfer laws lead to equations which have a lowers its temperature below the ambient or dry-bulb structural similarity to those derived from thermo te mperature _ The wet-bulb temperature attained dynamic reasoning as well as to those of empirical with the conventional psychrometer is dependent origin, they also involve the ratio of thermal to mass on many factors in addition to the moisture and diffusivities [3 , 11- 21]. Even these equations which te mperature state of the gas [1-4).1 Although at yield results in closer agreement with experimental te mpts have been made to develop a theory that data, do not completely depict all psychrometric w0l!ld correctly interrelate the parameters affecting behavior. For the water-air system, the ratio of thermal the behavior of the conventional psychrometer there to mass diffusivity is close to one , accounting, in part, is no theory which completely describes it ~ per for the nominal agreement between the predictions formance_ In the well-known convection or adiabatic based on the convection theory with those based on saturation theory [5- 10], the principles of classical heat and mass transfer laws_ In general, this ratio thermodynamics exclusively are used to derive a is greater than one [11, 221- formula that predicts the humidity of a moist gas from It would be advantageous to have an adequate wet- and dry-bulb thermometer measurements_ Un theoretical basis for the behavior of the conventional fortunately the conventional psychrometer, even psychrometer, but lacking a rational theory which under steady-state conditions, is an open system accurately and fully describes the operation of the undergoing a nonequilibrium process which cannot conventional psychrometer, one can invert the prob be depicted completely by classical thermodynamic lem and inquire whether a psychrometer can be built theory. It is fortuitous that the formulas so derived which will behave in accordance with the postulates of classical thermodynamic s_ It appears that such a
I Figures in brac kets indicate the literature references at the end of this paper. psychrometer can be designed and constructed and
28 3- 5760L-68-3 33 that its behavior can be predicted by thermodynamic h ~( P,Tw) =the enthalpy of 1 g of pure com reasoning and expressed in mathematical form. pressed liquid (or solid) of the vapor component at pressure P and tem perature Tw; 2. Theoretical Considerations he?, Tw, rw) =the enthalpy of (l+rw) g of gas mix ture saturated with respect to the Consider a closed system undergoing an isobaric second or vapor component at pres quasi-static process in which compressed liquid sure ? and saturation temperature (or solid) at pressure P and temperature Tw is intro Tw, that is, the enthalpy of a gas mix duced into a gas at pressure P, temperature T, and ture containing one gram of vapor-free mixing rati0 2 r to bring the gas adiabatically to satura gas and rw g of the vapor component; tion at pressure P, temperature Tw , and mixing ratio and rw. The term "gas" as used here and elsewhere in rw=rw(P, Tw)=the mass of vapor component of the this paper is intended to include a gaseous mixture gas mixture per unit mass of vapor of which one constituent or component is a permanent free gas of the mixture when it is gas or mixture of permanent gases and the second saturated with respect to the vapor constitutent or component is the vapor of the com component at pressure ? and tem pressed liquid involved in the psychrometric process perature Tw. and manifests itself as a product of evaporation. Since The "thermodynamic wet-bulb temperature" is the process is adiabatic and isobaric the sum of the defined [23] as the solution for Twin eq (1). enthalpies of the various phases within the system In order to facilitate the mathematical development are conserved, thus the initial and final enthalpies we introduce the following additional notation: are equal, leading to the following equation: t1T= (T- Tw) = The wet-bulb depression; h(P, T , r) = h(P, Tw, rw) - (rw - r) . h ~( P, Tw) (1) h(P, Tw, r)=the enthalpy of O+r) g of gas mixture at pressure?, temperature Tw where (the same as the "thermodynamic wet-bulb temperature" of the original h(P, T, r)=The enthalpy of (l+r) g of gas gas mixture), and mixing ratio r (the mixture at pressure P, temperature T same as the mixing ratio of the origi and mixing ratio r, that is, the en nal gas mixture); thalpy of a mixture consisting on 1 g h(P, T , 0) = h(P, T, r= 0) = the enthalpy of 1 g of of the vapor-free gas and r g of the the pure first (vapor-free) component vapor component; of the mixture at pressure P and r= the mass of vapor in the original gas temperature T;·· and mixture per unit mass of vapor-free h(P, Tw, 0) = h(P, Tw, r= 0) = the enthalpy ofl g of gas with which the vapor is associated; the pure first component of the mix ture at pressure P and temperature 2ln several of the engin eerin g disciplines r is call ed the humidity ratio. Tw . Let
F=F(?, T , Tw, r) = [he?, T , r) -he?, Tw, r)] (2) and
C. - [h(P, T , 0) -h(P, Tw, 0)] p,m- (T-Tw) (3) where
Cp = the specific heat at constant pressure of the pure vapor-free component.
Also let
C = [he?, T, r) -he?, Tw, r)] - [h(P, T , 0) -he?, Tw, 0)] pV,m r(T-Tw) (4) and
L = [h(P, Tw, rw) -h(P, Tw, r) - (rw-r)h~(? , Tw)] (5) V,T . (rw- r)
34 From the above definition, it will be clear that B = C/lV , III /Lv, r (10) C" , II/ represents the mean specific heat at constant pressure of the pure vapor-free first component over substituting these in eq (8), and solving it for r, one the temperature range from Tw to T. The entity Cpv, 11/ finds may be interpreted as the "effe ctive" specific heat at constant pressure P of the vapor component of the A6.T mixture taken as a mean over a temperature range (11) [1 + B6.11 from Tw to T and at a mixing ratio of r. Finally, Lv, r may be understood as the "effective" latent heat of where 6.T= T- Tw. vaporization (or sublimation) of the vapor component Solving eq (11) for A one obtains of the mixture at constant pressure P and constant te mperature Tw. It will be seen that Lv, r is taken as a mean while (rw-r) gram of vapor component A (12) evaporates into the gas mixture from a plane surface of its liquid phase per gram of first component. Both mixture and liquid must be at the same pressure P The "psychrometric [a ctor" A as defined by eq (9) and te mperature T w, the gas mixture having a mixing is identically equal to the " psychrome tric factor" A ra tio r initially and attaining a mixing ratio rw finally as given by eq (12). as a result of the process of evaporation. For the case where th e initial mixing ratio of the It should be noted that the "effective" specifi c heat gas is zero, eq (12) reduces to CPV, I/I and the "effective" latent heat of vaporization L v, r both differ from their counterparts pertine nt to A = ..0£.. (13) the pure phase of the second (vapor) component owing 6.T to the interactions between the molec ules of the first and second components of the gas mixture, and due If the vapor and the gas separately and admixed to other small effects [24]. with one another obey the ideal gas laws, eq (11) By adding to the func tion F each of the quantities becomes h(P, T , 0) and h(P, Tw , 0) , both with positive and negative signs, respectively, one obtains the useful rw A' 6.T (14) id e ntity r =(l + B' 6.T) (1 + B' 6.T)
F = [h(P , T, r) -h(P, Tw, r)] or, alternately, in terms of vapor pressure, = [h(P,T, r) - h(P, T , 0)]- [h(P,Tw, r) - h(P, Tw, 0)] + [h (P, T , O) - h(P, Tw, O)). (6) ew (P-e) (P - e) Ao6.T (15) e= (l + B' 6.T) (P-ew) (l + B' 6.T) When one subtracts h(? , T w , r) from both the left· hand and right-hand members of eq (1), it is obvious where that the left-hand member transform s to the function F. Therefore, the right-hand me mber of eq (1) minus Ao= My C~ (16) h (P, Tw, r) is also equal to F , so that we can equate Mv L~ this difference to eq (6) whic h yields the relationship
[h (P, Tw, rw) - h(P, Tw, r)] - (rw - r) h~( P , Tw) A'=~ (17) L'v =[h(P, T, r) - h(P, T, 0)] B ' = C~ v (18) , -[h(P, Tw r) - h(P, Tw , O)] L'v
+[h(P,T,O) - h(P,Tw, O)]. (7) and
Inspec tion reveals that the produc t (rw - r) Lv, l' is e = the partial pressure of the vapor component in equal to the left-hand member of eq (7), while the sum the original gas mixture; of the products (T - T w) Cp, 11/ and reT - T w) Cpv , 11/ is e = the saturation vapor pressure of the liquid phase equal to the right· hand member of eq (7). On making w of the vapor component at temperature Tit· ; these substitutions in eq (7) it transforms to e = the total pressure; C;JV= the pure phase specific heat of the vapor at (rw-r) LD ,,.= [Cp,m+rCpv, lI/] (T-Tw). (8) constant pressure; On introducing the "psychrometric factor" A and L ~= the pure phase latent heat of vaporization of the ratio B defined by the vapor; C;)= the specific heat of the vapor·free gas at constant A = Cp , m/Lv, r (9) pressure;
35 Ao= the so-called "psychrometric constant" (which liquids of higher vapor pressure. The discrepancy appears in most formulas for the conventional probably was due to in complete saturation and in com psychrometer [3 J); plete heat transfer between the gas and liquid rather My = the molecular weight of the vapor-free gas co m than lack of constancy of the wet-bulb tempcrature as ponent; and Lewis assumed. M,. = the molecular weight of the vapor component. Nanda and Kapur [28] performed similar experi ments, bubbling dried air into a Dewar containing such When e and elf are small compared to P and B'!:!..T is liquids as acetone, methyl alcohol, ethyl alcohol, and small compared to one, which is the case for the water butyl alcohol. After a considerable length of time, the air system at dry-bulb temperatures T up to about 45 liquid temperature approached the " thermodynamic °e, eq (15) reduces to wet-bulb temperature." We also repeated these experiments, and in doing e=e".-A,J)!:!..T (19) so found it necessary to use a vacuum-jac keted glass inlet tube, such as Lewis had used, for bubbling the which is identical to the classical equation often used gas through the liquid in the Dewar flask. With this to represent the behavior of the conventional psy inlet tube, which reduced precooling of the inlet gas chrometer. prior to discharge into the liquid, steady-state tem It does not appear feasible to construct a practical peratures of the liquids were obtained, which were psychrometer that is an embodiment of a closed system in close agreement with calculated "thermodynamic undergoing the ideal adiabatic isobaric saturation wet-bulb temperatures," provided the gas flow was process which serves as the basis of eq (1). On the very low and only after extended continuous flow, other hand, an open system undergoing a steady-flow usually hours. process would appear to be operationally feasible, and Although "thermodynamic wet-bulb temperatures" such a system was constructed and its performance could be obtained with the Dewar flask, the luw gas investigated. The aim was to approach ideal conditions flow rates, and the extremely long time necessary to as closely as practical, namely to bring compressed reach steady-state conditions at these flow rates, liquid (or solid) to pressure P and temperature Tw , to seemed to preclude its use as a practical instrument evaporate it into a gas stream at pressure P, tempera for measuring humidity. ture T and mixing ratio T , and to bring the gas adia Carrier and Lindsay [25], and Dropkin [14] con batically to saturation at pressure P, temperature T"., structed large scale, engineering-type apparatus for and mixing ratio Tw. This system then becomes an obtaining adiabatic saturation. The essential feature adiabatic saturator operating at constant pressure. If of these devices was the provision for passing air nothing enters to violate the conditions of eq (1), the over surfaces moistened with water that had been adiabatic saturator becomes an "adiabatic saturation precooled to , or close to, the wet-bulb temperature, psychrometer" since measured values of P, T, and Tw within well-insulated ducts. The experiments per can be inserted into eq (11) to obtain the mixing ratio formed by these investigators were limited to the of the entrant gas stream. It was realized that practical water-air system. and theoretical matters, such as heat exchanges due In 1961, J. D. Wentzel described a psychrometer to radiation and conduction, and pressure drop associ which apparently measured the "thermodynamic ated with flow , would be among the factors limiting the wet-bulb temperature" of water-air with high ac possibility of attaining the ideal, especially in view curacy [29]. In his instrument, Wentzel attempted of the desire to keep the apparatus simple for ease of to saturate adiabatically a stream of test air (whose construction. It was left, therefore, to experiment to humidity was to be measured) with water vapor in a serve as the indicator of how close the actual psychrom fashion that appeared to approach the idealized steady eter conformed to theory. flow adiabatic process. Basically his instrument con sisted of a vacuum-insulated glass tube, the inner 3. Background walls of which were silvered to reduce radiation effects. The tube was partially filled with a moistened natural In 1922, W. K. Lewis performed several experiments sponge through which the air flowed. Makeup water. in which a dried gas was bubbled through a volatile was added intermittantly, in one design, and con liquid in a Dewar flask containing glass beads, the tinuously in a second design. In the latter version, the gas being discharged into the liquid through a vacuum continuous flow of makeup water was precooled by jacketed glass inlet tube. For water-air, water-carbon an essentially equivalent instrument through which dioxide, toluol-air and chlorbenzol-air the gas sub part of the gas stream was channeled. To preclude stantially became saturated and the liquid (as well as the possibility of drying of the sponge, excess makeup the effluent gas) eventually reached a steady-state liquid was used. Wet-bulb temperatures were meas temperature that was essentially the "thermodynamic ured with thermocouples imbedded in the moistened wet-bulb temperature." The readings of wet-bulb sponge. Wet-bulb temperature measurements for temperature in the experiments using water, toluol the water-air system corresponded very closely to and chlorbenzol as the liquid were independent of " thermodynamic wet-bulb temperatures." It is well air velocity and of the amount of air contact with the known, however, that the wet-bulb temperature for liquid. This was not the case in the experiments with moist air as measured with a conventional psychrom-
36 J eter nominally is not very different from the " ther bulb temperatures" were closely approached with modynamic wet-bulb temperature" so that further various liquid-gas systems, as well as with water-air. demonstration is required to establish that a psy chrometer is undergoing a true thermodynamic wet bulb process. This could have been accomplished by 4. Description the use of liquid-gas systems other than water-air for which the wet-bulb temperature as indicated by The instrument is shown in fi gures 1 and 2. It a conventional psychrometer, and the " thermody consists of a vacuum-jacketed glass saturator tube, A, namic wet-bulb temperature" differ appreciably. that is surrounded by a glass Dewar fla sk, B. Within L. P . Harrison [26] has proposed three psychrometer ~he saturator tube is a thermocouple, C, for measuring designs for measuring " thermodynamic wet-bulb dry-bulb temperature, wicking, D, for saturating the temperature," each design involving the employment gas stream, and a feed tube, E , through which liquid of three concentric tubes so arranged as to insure is introduced for moistening the wicking. A thermo intimate contact between gas and liquid and therefore couple, F , for measuring wet-bulb te mperature is to insure adiabatic saturation. located beyond the outlet end of the saturator tube. We first duplicated Wentzel's instrument with some The saturator tube is centered and held in the Dewar modifications. Whereas Wentzel successfully had fl ask by a stopper, G. There is a pressure tap, H , at employed natural sponges as his saturating element, the outlet end of the saturator tube and an exit flow we were unsuccessful in the use not only of natural but line, I, through which the efflu ent gas leaves the also of artificial sponges because of the tendency for instrument. The test gas e nters at the inlet end of the the liquid to be blown out by the gas stream. Only when saturator tube, flows through the saturator tube, we fin all y resorted to cotton cheesecloth did the instru e merges at the outlet end of the saturator tube, re me nt operate sati sfactorily. Various liquid-gas systems verses direction, flows over the exterior surface of the were tried and although wet-bulb temperatures ap saturator tube and discharges through the exit flow proaching "thermodynamic wet-bulb temperatures" line and micrometer valve , ]. were obtained , these were not sufficiently close to one The main component is the saturator tube fabricated another to form the basis of an accurate measuring with double walls, with the space between the walls system. The best results were achieved with the evacuated and sealed. The tube is silvered to reduce water-air system. The major defect in the in strument radiation effects, is 13 in long, and has an o.d. of appeared to be the lack of sufficient precooling of the 1/2 in and an i.d. of 0.15 in. It is within this saturator liquid so that it would feed into the saturating element tube that the "thermodynamic wet-bulb process" at, or very close to, the " thermodynamic wet-bulb occurs. temperature." With the water-air system the operation The liquid feed system comprises a graduated reser· of an adiabatic saturation psychrometer is less sensi voir, K, a preliminary heat exchanger, L, a main heat tive to the liquid feed temperature than it is with some exchanger , M, and a feed tube, E. Liquid flows from other liquid-gas systems. the reservoir, through the heat exchangers, the feed We then developed an instrument utilizing vacuum tube, and onto the wicking. The reservoir is mounted jacketed glass tubes, as in the Wentzel instrument, but on a vertical rod. Its eleva ti on can be adjusted to pro employing a different saturating element and a novel vide the required head of liquid to maintain the fl ow feed arrangement that precools the liquid very close necessary for complete and continuous moistening of to the wet-bulb temperature. " Thermodynamic wet- the wicking. The preliminary heat exchanger is a 12-ft
8 D M E I I I I
, " , , "/, , , , , "
I I I· 9 ~------13 ------~ ~------1 4t ------~ ~------14~ ------~
DIMENSIONS IN INCH ES
FIGURE 1. Adiabatic psychrometer- principal section A. Vacuum-j ac keted glass saturator ru be; B. glass Dewar fl ask; C. Dry-bulb thermocouple; D. Cotton wicking; E. liquid feed tube; F. wel·bul b thermocoupl e ; C. saturator tube rubbe r stopper; L. preliminary heat e xchanger; M. main heat exc hanger; N. fl ow guide; O. fl ow g uid e cork stoppe r.
37 flow guide for channeling the gas over the surface of K- the main heat exchanger. It reduces the size of the annulus through which the gas flows and improves the heat transfer between the liquid in the main heat exchanger and the gas. The exit flow line is connected to a micrometer valve and then to a vacuum source, P. The pressure line is connected to an oil manometer, Q. which, in conjunction with a barometer which measures ambient atmospheric pressure, yields the absolute pressure at the outlet end of the saturator tube. A potentiometer and null detector are used to measure the emfs gen erated by the thermocouples. The saturator assembly is maintained in a horizontal orientation~ p The saturator tube is constructed with a vacuum jacket to reduce heat transfer between its interior FIGURE 2. Adiabatic psychrometer-schematic and its surroundings. The outer Dewar flask serves the purpose of providing additional thermal insulation c U~I~l e\ aD~ u~' ~;{~~l~e~i~ kr,~ ~~s E~ at i~I:~i'd'·f:~J)el ~I ~~; ~.~ S!e ~~b :i'i; t ~~~~~ o~~u ~r!; bet.b S !~I~;~~; tube rubber stopper; H. slatic pressure tap ; I. ex it fl ow tine: J. mi c rome ter exhaust valve: from the ambient atmosphere for the test gas. The K. graduated reservoir: L. prel imina ry heat exchanger: M. main heal exchanger : N. fl ow guide: O. fl ow guide cork s toppe r ; P. vacuum source; Q. o il manomete r. design of the liquid-feed tube and wicking combina tion is intended to provide a large evaporative area to the flowing gas while reducing as far as practical the length of poly tetra fluoroethylene tubing, with an o.d. of pressure drop and total liquid heat capacity. The liquid about 0.045 in and an i.d. of about 0.021 in, loosely feed heat exchanger provides for the automatic pre wound for 6 in around the outside of the saturator tube, cooling of the liquid by the gas which has been brought connected at one end to the reservoir and at the other to the wet-bulb temperature by the moistened wic king. end to the main heat exchanger. The latter is a 5-ft Counter flow of gas and liquid is used to obtain the length of stainless steel tubing, with an o.d. of 0.0355 in maximum heat exchange. It was intended that the and an i.d. of 0.023 in , wound into a 5/s-in diam helix total heat capacity of the heat exchanger and its con that fits over the outlet end of the saturator tube for a tained liquid should be as small as possible. The pre distance of 4 in. The feed tube is fabricated from 2 ft liminary liquid-feed heat exhanger is not considered of the same PTFE tubing as used in the preliminary to be part of the thermal capacity of the main heat heat exchanger. It is wound into a helix which fits exchanger and is a slight embellishment for heat ex inside the saturator tube and extends inward for 10 in change purposes. The liquid reservoir height ad from the outlet end. justment is used to control the rate of liquid feed. The feed tube is covered with a close-fitting sleeve Both thermocouples were located so as to be exposed of cotton wicking. One end of the sleeve terminates only to and in contact with the gas stream. 112 in inside the outlet end of the saturator tube; the other end is tied tightly with co tton thread immediately beyond the discharge port of the feed tube. 5. Operating Procedure The wet- and dry-bulb thermocouples are made from calibrated No. 40 copper and consta ntan wires The in strument is operated by establis hing a con encased in PTFE tubing like that described above. tinuous flow of sample gas and liquid. After s teady The dry-bulb thermocouple junction is located 1'/2 in state conditions are reached, th e wet- and dry- bulb inside the inlet e nd of the saturator tube and upstream te mperatures and the press ure are measured. of the wicking; the wet-bulb thermocouple junction The test gas is fed to th e saturator tube at atmos is located just beyond the outlet end of the saturator pheri c press ure. Because of the use of glass in the tube downstream of the wicking. Both junctions are construction of the saturator tube and the Dewar flask placed along the axis of the saturator tube. and the use of stoppers for assembling and sealing A silvered glass Dewar flas k, 12 in long and with an these compone nts, the maximum pressure within the i.d. of Pis in , encloses most of the saturator tube. psychrometer is limited to about 1 atm. The outlet port The saturator tube fits tightly within a concentric of the micrometer valve is attached to a vacuum source. hole in a No. 9 rubber stopper which, in turn, fits The mi cromete r valve is calibrated in terms of air snugly into the mouth of the Dewar flask. The two flow over the range 0 to 6.2 liters per minute. By means sets of thermocouple wires, the preliminary heat of a density correction, the equivale nt flow is obtained exhanger, the pressure line, and the exit gas flow line for any other gas. Thus, by an appropriate micrometer are fed separately through, and tightly fitted in, holes setting any desired fl ow within this range can be in the stopper. established through the psychrometer. Since the valve Within the Dewar flask is a glass lube, N, 9 inches functions as a variable critical flow orifice, the volu in length, 7/s-in o.d., and !lt6-in thick, that is, in turn, metri c fl ow through the psychrometer, for a given supported by a cork stopper, O. The saturator tube mi crometer setting, is essentially constant. with its associated components is positioned concen The heigh.t-of the reservoir is set so as to produce a trically inside the glass tube. The latter serves as a liquid flow rate that is approxi mately three times that
38 required to completely saturate the vapor-free test sible implications due to the restri cti on r = O will be gas_ This liquid flow rate is measured by timing the di scussed later. c hange in volume of the liquid in the graduated reser The followin g syste ms we re selected for the experi voir. If drying occurs in any part of the wicking, a me nts: water-air, wate r-hyd rogen, carbon tetrachloride te rn perature transient is propagated through the oxygen, carbon tetrac hl orid e- hydrogen, a nd toluene saturator that upsets the thermal equilibrium of the air. The gases were obtain ed from a commerc ial in strume nt and yie lds a n erroneous wet-b ulb te mpera source in s teel cylinde rs compre sed to a pressure of t ure. Excess liquid ins ures that the wicking is a lways about 120 atm. The carbon te trachl orid e was of spec co mple te ly moistened ; the excess is carried through tro grade_ the toluene of reagent grade, and the wate r the saturator by the fl ow of gas and coll ects in the of di stilled grade purity. These s ys te ms e ncompass De war fl ask where it can be dra ined ma nually or a uto a range of thermal to mass diffusivity ratios of 0.9 matically. Since the liquid e nters and e merges from to 4.5 as s hown in table 5. th e saturator tube at essenti ally wet-bulb te mpe rature, The experimental setup is s hown in fi gure 3. The the e nthalpies of the excess liquid fl owing into and out gas from a cylinder, R, was passed through a high of the saturator are essentiall y equal and therefore do pressure reducer , S, and a low pressure reducer, T , not contribute to the overa ll e nth a lp y bala nce as in series, a drier fill ed with phos phorous pentoxide, gi ve n in eq (1). U, and a s tainl ess steel heat exchanger, Y, immersed in a te mpe rature-controlled liquid bath, W , a nd then 5.1 . Tests fed into the psychrometer, X, at a pressure of about 1 atm. The desired gas fl ow rate was obtained b y th e S in ce eq (1) re presents an interre lati on among appropriate setting of th e mi c romete r on the exhaus t para me te rs P, T, T" .. and r s uch th a t I(P, T, Til" r ) = 0, va lve, J. The reservo ir, K, was fill ed with the test the n if any three pa rameters, say P, T, a nd r are meas liquid and it s elevati on adjus ted so that the liquid ured a nd inserted into the equa ti on, the fourth, Til" How rate was a pproximate ly three times as great as can be calculated. If, in addition , a measure me nt is th at calcul ated as necessary to complete ly saturate also made of Til', the calculat ed a nd observed " the rmo the test l!as at th e wet-bulb te mperature. d yna mi c wet-bulb te mpe ratures" can be co mpared. T ests were a lso performed to determine the s peed Such a co mparison offe rs a measure of the co nformance of response of the instrument. U in g a ir as the sample of psychrome te r be havior with theory. gas, and water as th e liquid, th e psychrometer wa s Equation (12) Ill ay be expressed in th e form s ubj ected to a nominal s te p-func ti on cha nge in mixing ratio at a dry-bulb tempe rature of 25 °C and at a n a m C/I. 111 _ rll· - r[l + B6.TI 1:;";- 6.T (20) bi e nt atmosphe ri c pressure of abou t 1 bar. Dry air was fed to the psychro me ter. Aft e r s teady-stat e con ditions we re reached , the conn ecti on feedin g th e dry in wh ich the right- a nd left -hand sides a re diffe re nt air to the inlet of the saturator tube was quic kly re fun c ti ons of the same paramete rs, tha t is, moved a nd ambie nt (roo m) air was drawn in producing a n in c rease in mixin g ratio. The procedure was then AdP, T, Til'. r)= AAP, T, T", r). (2 1) reve rsed producing a decrease in mixing ratio. The e mf from the wet-bulb thermocouple was fed to a pre By in serting the same set of measure me nts of the cis ion pote ntiometer. The unba la nce of the poten para mete rs (P, T, T,C, r) into AI a nd A1 these two func ti ometer was amplifi ed a nd recorded as a function of ti ons can be calcul ated a nd compared. S uch a co m time . After nulling the potentiometer for the steady parison offe rs an alternate me thod of checking whether state initial wet-bulb te mperature condition, a trace the psychrometer performs in accord ance with theory. was obtained of the wet-b ulb te mpe rature cha nge s hould be recognized that A I and A~ are alt e rn ate It produced by the s te p-function change in mixin g ratio. expressions of the " psychrometri c factor." A seri es of experime nts was performed with the psychrometer, with various liquid-gas systems. to 5.2. Results obtain experimental or observ ed values of the wet bulb te mperature whic h is give n the notation (T,,)obS' A compari son is s hown in table 1 between the With the same values of paramete rs fl , T, and r . the observed and calculated " the rmodynamic wet-bulb " th ermod ynamic wet-bulb te mpera ture" was cal te mper atures," (TII")ohs and (T"')ea 'c' for the several c ulated. To differentiate it from the observed va lu e liquid-gas syste ms that were investi gated. The a bsolute it is given the notation (T")ca'e' Because of th e diffi pressures P in the region of the wet-bulb thermocouple cully of generating vapor·gas mixturcs of known mixing are giv e n in column 1. Column 2 li sts the approximate ratios to s uppl y to the psychromete r, onl y dry, vapor flow rates of the gas at the inlet end of the psychrom free gases were used. Thus, in each case the mixing ete r, that is, at te mperature T. Columns 3 and 4 li s t rati o r of the gas was zero. All ex periments we re per the observed (measured) dry- and wet-b ulb tem pera formed at room te mperature (about 25 °C), except for tu res. The calculated wet-bulb temperatures, obtained four test points with water-air which were perform ed by solving eq (23) or (24) (see appendix) for Tn', are at about 37 °C, and at atmospheric pressure (a bout give n in column 5. The differe nces betwee n the ob 1 bar). The How rate of the test gas mixt ure was varied served and calculated wet-bulb tem peratures, ove r th e range 0.8 to 6.2 lit ers per minute . The pos- r(TII")Obs-(T"')calei, are ta bulat ed in column 6.
39 R '\ ----EJ I AA BB
-p
. FIGURE 3. Test setup - schematic J: mlC~omet!!r exhaust valve; K. graduated reservoir; P. vacuum spurce; Q. oil manometer' R. compressed gas cylmder., S: high pressure reducer; T. low pressure reducer; U. dner; V. heat exchanger; W. temperature· con· t~olled liqUid hath; X. psychrometer; Y. reference junction ice bath; Z. thermocouple selector switch; AA. pre· elson laboratory potentiometer; BB. null indicator.
Columns 7 and 8 of table 1 give values of the "psy- The parameters used in the computation of (T w)cale, A 1 and A2 are listed in column of table f rw p , In • 1 2. c h rometnc. actor"A 2 = AT an d A 1 = -- C respectiveI y, '-1 Lv, r The nominal magnitudes of the parameters are given in for the various liquid-gas systems studied. The differ column 2. Estimates of the systematic and random ences (A 2 - A I) are given in column 9 while the per- errors in these parameters are given in columns 3 and 4 while the corresponding systematic and random centage difference (A2 ~2Al) 100 are given in column errors in the wet-bulb temperature difference 10. [(Tw)ObS - (Tw)calcJ and in the psychrometric factor Since in this imperfect world one cannot expect difference (A2 - AI) produced by the estimated perfect agreement between experimental and theoreti errors in these parameters are given in columns cal values, it is desirable to have some criteria by 5, 6, 7, and 8. Thus, for example, an estimated system which the reasonableness of the agreement can be atic error of 0.01 deg C in T for the water-air sys· assessed. An error analysis was therefore made to tem produces a corresponding systematic error or obtain estimates of the accuracy of the calculated 0.005 deg C in [(T W)ObS - (Tw)calc] in the water-air "thermodynamic wet-bulb temperature" using the system. The estimated overall systematic error in observed, or measured parameters P, T, and r. It is [(T w)obs - (Tw)calc] was obtained by summing the indi apparent that an iterative method must be used to vidual systematic errors listed in column 5. Simi solve eq (23) or (24) for Tw- Furthermore, the param larly the estimated overall systematic error in (A2 - A I) was obtained by summing the individual systematic eters P, T, Tw , and r must be known or assumed in order to obtain values of the enthalpy functions errors in column 7. The estimated overall random error in [(T w)Obs - (Tw)calc] and in (A 2 - A 1) was obtained h(P, T, r), h(P, Tw, r), h(P, Tw, rw) and h~(P, Tw), the by computing the root-mean-square value of the in latent heat of vaporization function L~(Tw) and the saturation mixing ratio function rw(P, Tw). Not only ~ividual random errors in columns 6 and 8, respec do the measurement errors in P, T, and r enter into tively. The estimated overall errors may be consid ered as guesses of the differences between (Tw)ObS estimation of the error in (Tw)calc, but experimental and other systematic uncertainties in the enthalpies, latent and (Tw)cal c and between A2 and A 1 which may be heats of vaporization and saturation mixing ratios must expected to occur due to systematic and random be accounted for. A similar analysis was made to errors, provided the psychrometer otherwise acted in accordance with eq (1). obtain estimates of the accuracy of the psychro Table 3 lists, for each liquid-gas system, the aver metric factors A 1 and A2 using the observed parameters age of [(T W)ObS - (Tw)calc] and an estimate of the stand P, T, Tw , and r. Details of the analyses are given in the ard deviation of the average. Estimates of the over appendix, along with the sources of the thermody all systematic error and the overall random error namic data and physical constants used in the calcula given in table 2, are repeated here for convenienc~ tions. The results of the analyses are presented in in making comparisons. Table 4 gives similar values tables 2, 3, and 4. for (A 2 -A 1) . 40 TABLE 1. Comparison between wet-bulb temperatures and psycltrom~t,.ic factors
Wet-bulb te mperature Ps ychrometric fa cto r Dr y·bulb I'ressure Flow tem perature PcrcentH ge /' T Observ ed Differe nce differe nce (Tu')ubS (II, - A,) IA ,-A, ) --x 1011 A,
Ba rs Lit er per dog C deg C deg C dog C lO -'/deg C lO -'/deg C 10 ' /deg C % minute
Water - Air
0.974.5 1.4 24.80 7. 87 7.86 11.01 40.65 40.57 0.08 0.2 .9737 1.4 24.73 7.81 7.82 -.11 1 40'. .54 40 ..57 - .03 - .1 .98 16 1.4 24.62 7.80 7.83 - .03 40.42 40 ..57 - .15 - .I ~ .9806 1.4 24.65 7. 82 7.84 - .02 40.49 40. 57 - .08 - .2 1.0002 1. 4 25 . 11 8.24 8.2 1 .03 40.76 40.59 . 17 .4 0.9943 2. 1 37. 07 13.2.5 13.26 -.01 40.71 40. 75 - .04 - . 1 .9948 2. 1 37. 01 13. 19 13.24 -.05 40. 53 40.75 - .22 - 5 .9943 2. 1 37. 02 13.27 13.24 .03 40.88 40. 7.5 . 13 .3 0.9978 2. 1 37.02 13.23 13.27 -.04 40 . .56 40.75 - . Il) . .0 1.0000 2. 1 24.98 8. 1.5 8.14 .0 1 40.61 40 ..08 .03 . 1 1.0005 2. 1 25.02 8. 16 8. 17 -.01 40.55 40 .58 - .03 - . 1 1.0008 2. 1 25.02 8. 18 8.17 .01 40.64 '10.59 .05 . 1 1.0008 2. 1 25.08 8.22 8.20 .02 40.70 40.59 . 11 .3 1.0007 2. 1 25. 17 8.2.0 8.24 .01 40.65 40.59 .06 . 1 0.98 18 6.2 24.88 8.07 7.95 . 12 4 1.19 40.58 .6 1 1..0 .9829 6.2 201.85- 8. 10 7.95, .1 5 41.38 40 ..08 .80 l.l)
\Valer- Hydrogen
0.9718 5. 2 24.40 7. 60 7.58 0.02 576.8 575.0 1.8 0.3 .9807 5.2 24.29 7.57 7.60 - .03 573. 1 575.0 - I.l) - .:1 .9823 5.2 2'1.25 7.56 7.59 -.03 572 .8 575.0 - 2.2 - .4 .98S! 0.2 24 .40 7. 63 7. 68 - .05 57 1. 2 575.0 - 3.8 - .7
Carbon tel rachloride - Oxygen
I 0.l)l)29 1.3 24.52 - 8.50 - 8.52 0.02 416.8 416.1 0. 7 0.2 .97 14 I.l) 24.67 - 8.73 - 8.72 -.01 415.6 416.0 - .'I - . 1 .9876 1. 9 24.66 - 8. 56 - 8.53 -.03 415. 1 416. 1 - 1.11 - .2 .9878 1.9 24. 45 - 8.66 - 8.60 - .06 41 3.8 416 .0 - 2.2 - .5 .9870 1.9 24.41 - 8. 69 - 8.62 - .07 41 3.6 416.0 - 2.4 - .6 1.0114 0.8 24.26 - 8. 17 - 8.39 .22 424.8 416. ~ 8.5 2. 0
Carbon lelrachl oricie - Ii ydro!!c n
1.006 1 2. 1 23.93 - 8.71 - 8.83 0.12 6.5 19 6.4.5 1 68 1.0 0.9970 2. 1 23.82 - 8.83 - 8.97 . 14 6.531 6.4.50 8 1 1. 2 .9839 2. 9 24. 18 - 8.96 - 9.00 .04 6.471 6.449 22 .3 .9843 2.9 24.20 - 8.98 - 8.l)l) .01 6 . 4S~ 6.449 4 . 1 .9848 2. lJ 24. 12 - 9.01 - 9.0 1 .011 6.447 6.448 - I - .0
T ~l l u e n c - Air ----- O.l)l)UI 1.4 2.0.47 6.79 6.84 - 0.0.0 236.8 1:38.2 - IA - 0.6 .t)l)H6 1.4 2.0. 37 6.74 6.80 - .06 236.5 238.2 - 1. 7 -.7 .t-}l)23 1.4 2S. 15 6.65 6.64 .01 238.4 238 .2 11. 2 . 1 .CJ930 1.4 25. 13 6.6S 6.64 .111 238 . .0 238.2 0.3 . 1 .9764 2. 1 2.0.58 6.6.0 6.70 - .11.0 2:16.8 238.2 - !.4 - .6 .'J784 2. 1 2.0 ..54 6.62 6.70 - .118 236.0 238.2 - 2.2 - .lJ 1.1111.56 0.8 25.09 6.911 6 .73 . 17 242.9 238.3 4.6 I.lJ I.IX)7S 0.8 24.98 6.90 6.70 .20 243. l) 238 ..3 5. 6 2.3
If the errors in (Tw)ObS and (Tw)calc , or in Az and A I , It can be observed from table 3 th at the average were sole ly random, then the average of the appropriate values of [(T',.)ObS - (T"')ca ic i are smaller than the diffe re nce, for a given liquid-gas system, would tend estimates of the overall systematic e rrors of [(T w)ObS tuward zero. Since th e averages are not equal to zero, - (TII')ca lcJ. This is also the case for (A z - A I) as shown one would ex pect th at these values are experime ntal in table 4, This is probably due to an overly conserv a measures of the syste matic errors and should therefore tive estimate of the individual syste matic e rrors of have the same magnitudes as the estimates of the over the parameters (especiall y j;,.) and the fact that s um all syste matic errors. The standard deviations of the min g the corresponding individual syste matic errors diffe re nces about th ese ave rages, on th e other hand, of the appropriate differences gives a maximum. are indicators of th e exp erimental random errors It can be observed further from tables 3 and 4 and so, correspondin gly, should have a close rela that the estimates of the standard deviations are ti onship to the estimates of the overall random errors. considerably greater than th e estimates of the over-
41 TABLE 2 . Error analysis
Estim ated error of Estimated error of Estimated error of the parame ter [(T".),,,-(T,,.),,,,) (A,- A,) Nomin al due to parameter error due to parameter error magnitude Parameter of paramete r Systematic Random Syste matic Random Systematic Random*
deg C deg C IO -'jdeg C 1O -'jdeg C
Water-Air
IT ... )",IS ...... 'c. .. 8. 0.01 0.Dl5 0.010 0.015 0.052 0.08 ;'c. .. 25. .01 .024 .005 .011 .024 .06 1.0 .0002 .002 .01 g M, ...... i! 010' " 18.01534 .00006 .000 .000 M".... ---'-- 28.9645 .OO()O9 .000 .000 g mul j;, ... 1.004 .0008 .006 .033 e" ...... bar. . 0.0107 .0000043 .003 .016 J C,...... 1.0 .00036 .003 .0 15 g ' (: ! "~ ...... 33 . .025 .000 .000 h,.,. ~ 2.5 16 .084 .000 .001 Estimated overall error .027 .019 .14 .10 - ---- Water-Hydrogen
T"...... 'c.. 8 . 0.01 0.015 0.010 0.015 0.74 1.11
T ...... ' ...... ' (: .. 25. .01 .024 .005 .01 I .35 0.83 I' ...... bar. .. 1.0 .01 .0002 .002 . 12 M,...... ---L. 18.01534 .00006 .000 .00 g: mol ----L M!I" ...... 2.01594 .00001 .000 .010 g mul I. .005 .039 2.91 0.0104 .0000042 .003 .23 14.2 .00042 .000 .02
2.483 1.76 .005 .40 Estimate d uverall e rrur. . .062 .020 4.65 1. 39
Carbon Tetrac hluride-Oxygen
- I). 0.01 0.015 0.010 0.015 0. 37 0.56 25. .01 .024 .003 .IX)8 .12 .31 1.0 .0002 .002 .09 vi, ... 53.82315 .002 .000 00 :,! mol" M!/ ...... --L 31.9988 .0001 .000 .00 ~ mol j;, ...... I. .005 .057 2. 14 t'"...... bar.. 0.027 .00OII):l .038 1.46 J C,...... 92 .000167 .002 0.9 " ' <: 214. 1.09 .055 2. 14 Estimated ov erall e rrur .. .165 .017 6.32 .65
Carbun Te lrachJuride- Hydrogen
- I). 0.01 0.Dl5 0.0 10 0.015 6.0 8,y 25. .01 .024 .003 .008 2.0 4.7 /.) ...... bar ... 1.0 .0002 .002 .1 J.3 M, ...... ~ 153.82315 .002 .000 .1 ~ mul 1tiJ" , ...... -- 2.01594 .00001 .000 .0 g mol I. .005 .056 33.2 0.027 .000091 .038 22.6 13.4 .00406 .000 0.2
214. 1.1)9 .0,54 32.9 Estimated overall error. .16 1 .017 n.o 10.1
Toulcne - Air
T", ...... '<:. 7. 0.01 0.015 0.010 0.01,5 0.27 0.40 T ...... •...... ' <:. I 25. .01 .024 .004 .0 10 .13 .31 42 TABLE 2. Error analysis-Continued
Estimated error of Estimated error of ES linl31ed e rro r of the parameter [(Tw)Obs -(T II')caLc] (A, - A ,) No minal due to parame te r error due to Iw ra me ler e rror mag~}lude 1-----,----+-----,----+ ----,----- Parameter parameter Systematic Random Systematic Random Systematic Rando m *
deg C deg C
Toul ene Air-Continued
I' ...... bar .. 1.0 .0002 .002 .05 II ,. 92. 14181 .00008 .000 .00 g mol g 28.9645 .0009 .000 .01 g mol I. .005 .049 1.20 ew•· ...... • ...... bar. . 0.014 .0000 14 .010 .24 J (;11 ...... ••• .. 1.00 .00036 .002 .07 ~ . (: J I"" ...... 423. .88 .02 1 .40 Estimated Hverall e rrur.. .096 .018 2.32 .51
*ESlimaled sta ndard d eviation of an observatio n.
'fABLE 3. SlLInm.ary oj wet·bu.lb temperature differences e mfs were not read simultaneously and sin ce the [(T w)f!IJ.'i - (Tw)('al(' ] wet·bulb thermocouple does not respond to changes in inlet temperature as rapidly as does the dry·bulb S tandard Estimated Estimated Estimated Rcjectiull deviat iun overall uve rall total c rit e rion th ermoco uple, it. is likely that the actual random System Av c ra:.:c of the dif· system· random te mperature errors were greater than that estimated. fercnces atle e rror e rrur* about the That the standard deviation was approximately two· ave ra:.:c c., c., IC.,+ C.,) (""' + 3C.,·) to three·fold the estimated overall (static) random e rror, does not seem disturbing, but does indicate de~ C de~ C de~ C del! C de~ C de!!C II ~ O · A i r + 0.015 0.053 0.027 O.O IY O.O"~ 0.084 that some contributory effects were not accounted II ~ O · Air - .003 .026 .027 .0 1Y .04,6 for. d~('s triclf'( 1 tlow) II ,O·H, - .02 1 .033 .062 .020 .082 . 122 Examining the data in table 1, one find s that there LClrO:! +.01.3 . 108 . 165 .0 17 . 182 .2 16 en,.o, - .02Y .0:l5 .165 .0 17 . 182 are seve ral sets of measure me nts which yielded ex· (I{ cstricted fl ow) U :I, H, + .060 .064 . 161 .0 17 . 178 .2 12 cessiv ely large individual diffe rences 111 [(T"')ObS C ; II ~ · Air + .0 18 .109 .01)6 .0 18 . 114 .150 - (T,r)calc l· (:+ tM· J\ir - .038 .042 .0% .0 18 . 11 4 d~ f's lri( ' lt'd How) The criterion was establis hed to reject any diffe r
*Estima ted standard deviation of an ubservulioll. e nce which exceeded the s um of the estimated over· all systematic error plus three times the estimated overall random error in [(T w)ObS - (T w)ca lc I. It was TABLE 4. Su.m mary oj psychrometric Jactor differences (A, - A,) assumed that s uc h large - differe nces re prese nted anomalous behavior of th e psychrometer. The appli· S tandard BeJative Estimated Estimated Estimated de vi ation avera~e overa ll overall total cati on of this criterion led to the rejection of two sets Syste m Avera~e of the dif· syste m· random e rror of data for the water·air system, one set of data for ferclI('cs alie e rror error* about the the carbon te trac hloride·oxygen system, and two sets avera~e c.., c., (C..+ I> ,) of data for the tolue ne·air system. These rejected sets of data included all ex perim ents performed at 10 · "/
It appears that the rejec tion process eliminated 150 both low and high flow-de pe ndent syste matic errors.
This is to be expected since at very low flows heat if) o losses to the ambient atmos phere become a noti ce 6 120 u able fraction of the heat supplied by the test gas. w if) At very high flows , incomplete saturation and incom f- plete heat exchange apparently occur. Z 90 f'O if) Corrections or error estimates could be made for Z radiative or conductive heat losses, incomplete o WET TO ORY ~ 60 saturation, change of kinetic energy of the gas stream, :;; heat supplied by incoming liquid or other factors f- that mi ght tend to affect the performance of the 30 psychrometer. In designing this instrument, an at te mpt was made to make these sources of error as negligible as feasible, so that corrections would not o 2 3 4 5 need to be applied. Since the purpose of these tests FLOW, LI TERS PE R MINU T ES was to determine how well the instrume nt actually performed its intended function as an adiabati c FIGURE 4. Time constant versus inLet gas /low rate for water-air saturation psychrometer , such corrections were not system. made in this evaluation. Though on the average the measured wet-bulb It is important to reiterate that the adiabatic satura te mperatures differ little from the calculated wet tion psychrometer behaves very differently from con bulb temperatures, there is a prevalence for the meas ventional types of psychrometers. This is shown in ured te mperature to be lower than the calculated table 5 whic h compares the psychrome tric factor te mperature for the "restricted flow" cases. This ratios A2/A J at r = O obtained at NBS with the adia probably stems from the fac t that the true f w-factor batic saturation psychrometer and with three types is greater than unity whereas a value of one was used of conve ntional thermocouple psychrometers cor for all syste ms except water-air in determining (Tw)ca lc' rected for radiation losses; it also li sts ra tios based For the water-air system, for which the f w-factor is on results re ported by other investi gators on conven known and therefore was used, (Tw) calc is much closer tional psychrometers. The ratio is essentially unity to (TW )ObS on the average than for any other syste m. for the adiabati c saturation psychrometer for the fiv e The response time traces obtained appeared to syste ms li sted ; it differs significantly fro m unity for have the general shape of expone ntial functions th e conv e ntional types of psychrometer , although as one would expect. The time co nstant T was ob for the water-air syste m the magnitude of the differ tained by measuring the time required for the wet ence I S s maller than for the other system s. bulb temperature to undergo 63 percent of its total change for each test condition. Figure 4 is a plot of these meas ured time constants against gas fl ow TABLE 5. TypicaL psychrometer pel!orl7la nce rate for the two conditions tested. The time constant is a function of gas flow rate. At flow rates of· 3.75 Rat io uf psychromet ri c facturs. A:!/A I to 5.2 liters per minute the time constant is about Rat io of N BS instrume nt s Othe r in stru m e nts 3/4 of a minute. the rmal - ----.---.--- 1-- -,----,-- Syste m to mass Although the te mperature of the liquid at the point diffu siv- Ad iabatic Thermo- Ther mo- Thermo- ities s allu"a· cu u ple co u ple couple Arnuld Sher- Le wi s wh ere it discharges onto the wicking was not meas lion ps y- psy- psy- psy- [ II ]" wuud [ 13] ch rom- c h ru m- c hro m - chrom- [ 12] ured, several calculations were made to obtain esti e ler ;! e ler A 10 ele r B IJ e le r e" mates of how close this te mperature approached the " thermodynamic wet-bulb temperature." For ex 1I ,0 ·Air 0.9 1.000 1.1 4 1.04 0.95 1.21 11 ,0 ·11 , 1.7 0.997 1.64 1.47 1. 53 ample, with water flowing at a rate calculated to be CC L,·O, 3.0 .997 2.33 2.23 three-fold that required to saturate an air flow of 1112 CC I,- II , 4.5 1.005 2.79 C, H ... ·Air 2.6 liters per minute at inlet conditions of zero mixing 0.996 2.07 1.96 1. 77 2.08 2.5 ratio , 25 °C dry- bulb te mperature, and 1 bar press ure, a Shielded ui!ainst rad iation . 10 Corrected fo r radiat ion. the liquid feed te mpe rature was calculated to be 0. 2 °C hi ghe r than " thermodynamic wet-bulb tempera ture." This, it was estimated, would elevate the we t 6. Discussion and Conclusions bulb te mperature by approximately 0.008 0c. If the inlet relative humidity of the gas were hi gher, the The theore tical basis governing the operation of other inlet and fl ow conditions re maining unchanged, this instrument has been de monstrated at room te m the absolute te mperature error in the liquid feed would perature, atmospheric pressure, and ove r the flow be less, but th e percentage error in the ex perimental range of 1.3 through 5.3 liters per minute, by tests psychrometric factor, would be the same. with several liquid-gas systems subject to the re-
44 stnctJOn that the data were limited to the condition a total pressure of 1 bar, a nd using the above error in r = O. Since zero mixing ratio produces the maximum wet-bulb temperature, it is estimated that the psy· wet·bulb depression for any giv e n dry· bulb te mpe ra chrometer can be used to de termine the relative ture, and since s uch effects as radiative and conduc humidity to within 1/4 percent. Table 6 gi ves the error tive heat losses tend to have a greater influence with estimates in both the mixing ratio and relatIve humidity increasing depression, the r= 0 condition subjects the determination at various inle t relative humidities. psychrometer to its severest ex perimental test. Use of the gas te mperature just beyond the outlet end of T ABLE 6. Estimated instrument error Jo r water vapor·air system at the saturator tube rather than the temperature of the 25 °C, 1 bar pressure and various relative humidities moistened wic king as the wet-bulb temperature further increases the assurance that this instrument is producing "thermodynamic wet-bulb temperatures." RH t:.r t:.RH Sin ce essentially all cooling of the incoming gas occurs by heat transfer from the gas to the moistened wi ck % g vapor/g vapor· free gas % ing, the average temperature of the moistened wi ck in g must of necessity be equal to or less than the a ve rage te mperature of the exit gas. It is possible 0 0.000025 0.13 20 .000029 .1 5 under some circumstances (for example, where the 40 .000034 .17 ratio of thermal to mass diffusivity is less tha n 1) for 60 .000038 .19 the moi stened wi cking to be cooled below the " thermo 80 .000043 .21 dynamic wet·bulb te mpe rature," but it is extre mely 100 .000049 .23 unlikely that the average temperature of the exit gas I could be as low as the " thermodynamic wet·bulb te m perature" without satisfying the postulates that form The suggestions and cn tlclsms of L. P. Harrison, the theoretical basis for eq (1). ESSA, W eather Bureau, Silver Spring, Md., are Although the intended use of this instrument is to gratefully acknowledged. measure the water vapor content of gases, it is possible to use it for the determination of other vapors in gases and perhaps for the determination of fw for particular 7. Appendix. Computations and Sources of vapor·gas combinations. The latter might be done Constants by controlling inlet gas te mperatures in such a way as to produce wet· bulb temperatures which corre (Tw)calc was computed for each experimental point spond to those at which the vapor pressure and by solving one of the following equations in a n itera· late nt heat of evaporation of the liquid are well known. tive manner, using measured values of ? and T: Due to the difficulty of producing known vapor h(?, T , 0) = h (? , Tw, rw) - rwh'w (?, Tw) (22) concentrations in gases other than zero, this instru ment was only tested at the condition r= O. Its per· he?, T, 0) = h e?, Tw, 0) r wL~ . (23) formance characteristics, therefore, have been + demonstrated only at this condition. W e believe A2 was computed for each experimental point equat· however, that the characteri stics would not be al· ing A2 to A in eq (13) into whic h the measured values tered significantly were the psychrometer operated at of P , T, and Tw were substituted. Al was computed for r > O. Furthermore, as mentioned above, for any each experimental point by using one of the followin g give n dry·bulb temperature , r= 0 produces the mini equations into which the measured values of ?, mum wet· bulb temperature and subjects the psy· r, and Tw were sU9stituted; c hrometer to the maximum radiative and conductive heat losses, and hence is the most severe condition under whic h to test the be havior of a psychrometer. AI= rw[h(P, T, 0) - he?, Tw, O)} r, It is of interest to predict how well one could !:J.T[h(P, Tw, rw) - h (P, Tw, 0) - rwhw( P , TW)J measure the water vapor conte nt of air with this (24) psychrometer. Whereas the magnitude of the error in wet· bulb temperature probably is related directly A - [h(P, T, 0) - h(P, Tw, 0)] (25) to the difference between wet- and dry-bulb te mpe ra 1 - !:J.TL ~ tures, we will use for our prediction the error obtained at r = 0 which is in all likelihood maximum since the where Al is the equivalent of A in e q (9). wet- a nd dry-b ulb temperature difference is maximum, Equations (22) and (24) were used for the water· air and handle it as though it were a fixed error although system and are exact. Equations (23) and (25) are it is likely smalle r at higher relative humidities. For approximations and were used for all other syste ms our estimate of this error we will use the average because neither the gas mixture e nthalpy h (P, T w, rw) value of [(Tw)o bs - (Tw)ca lc] plus one standard devia nor the "effective" late nt heat of vaporization Lv, ,. for ti on of this quantity obtained from the "restricted these systems was known. fl ow" test points. This should give us a one·sigma error In all cases rw was determined by solution of the estimate. Assuming a dry· bulb temperature of 25 °e, following equation: 45 lated from the following equation given by Hilde (26) brand [36]: where fw= a function of pressure and temperature Cw= Antilog [6 .89406 - 22~~i~·!8T) mm Hg for a given liquid-gas system.3 Each of the individual errors in (Tw)calc is associ or ated with an error in one of the parameters entering into its calculation. The error in (Tw)calc was obtained 1219.58 by solving eq (22) or (23), as appropriate, using the ew = 0.0013332 Antilog [6.~9406 227.16+1') bars. parameter value plus its estimated error in the cal culation and subtracting (Tw)calc from the result. The The estimated errors in these parameters are given in individual errors in (A 2 -At ) were obtained by solving table 2. equations (13) and (24) or (25) as appropriate, using C arbon Tetrachloride-Hydrogen System. Enthalpies the parameter value plus its estimated error in the were obtained as in the water-hydrogen system and calculation along with the values of (Tw)calc obtained all other parameters were obtained as in the carbon from prior computation. The solution of these equa tetrachloride-oxygen system. The estimated errors in tions gives the error directly since A2 - A t = 0 at these parameters are given in table 2. . (Tw)calc when there are no errors_ Toluene-Air System. h(P, 1',0) and h(P, Tw, 0) were The results of the error computations are given in obtained for vapor-free air by linear interpolation of table 2. tabulated values given by Hilsenrath [33]. Values of Water-Air System. h(P, T, r), h(P, Tw, r) and h(P, ew were obtained from the equation of Rossini [37]: T w, rw) were obtained by solution of the following equation: 1344.800 ] cw=Antilog [ 6.95464-219.482+Tw mmHg h=~ R [1'+ ~ r (T+ 1354. 74)]+ ~h %: or
R = 0.068557 ITcal-K- t(g dry air)- t or 0.28703 j-K- t ew=0.0013332 Antlog'1 [6 .9 5464-219.482+T1344.800 w] b ars. (g dry air)- '. and ~h was obtained from table 85 of the Smith A value of unity was assigned to fw and L ~ was com sonian Meterological Tables [31]. puted from the equation given by Scott [38]: Values of h~ were linearly interpolated from a table given by Goff [24] and values of fw were obtained by L' = 11637 -4.823 Tw-1.260 X 1O -2T~ linear interpolation in both T and P from values given v 92.141 in Table 89 of the Smithsonian Meteorological Tables where Tw is given in degrees Kelvin. According to [31]. The saturation vapor pressure of water was Scott, this formula is applicable over the temperature obtained by solution of an equation given by Goff [32]. range of 298 to 410 oK. However, since it was used to The estimated errors in these parameters are given extrapolate values of L ~ at 280 oK, allowance for this in table 2. fact was made in estimating the error in L~. The Watcr-Hydrogen System. h(P, T, 0) and h(P, T". , 0) estimated errors in these parameters are given in were obtained for vapor-free hydrogen by linear table 2. temperature interpolation of the tabulated values given by Hilsenrath [33]. Values of L~ were obtained 8. References from steam tables [34]. In the absence of data on the [1] Monteith, J. L. , Error and Accuracy in Thermocouple Psy factor fw at the experimental test conditions, a value of chrometry, Proceedings of the Physical Society, B LXVII, unity was assumed for fw. Values of ew were obtained 217 (1954). [2] Bindon, H. H., A Critical Revi ew of Tables and Charts Used in the same manner as with the water-air system. The in Psychrometry, Humidity and Moisture 1, 3 (Reinhold estimated errors in these parameters are given in Publishing Corp. , New York, 1965). table 2. [3] Harrison, L. P ., Some Fundamental Considerations Regarding Psychrometry, Humidity and Moisture 3, 71 (Reinhold Pub· Carbon Tetrachloride-Oxygen System. h(P, T, 0) lishing Corp., New York, 1965). and h (P, l'w 0) were obtained for vapor-free oxygen [4] Wylie, R. G. , P sychrometry, Report PA-4, Commonwealth of by linear temperature interpolation of tabulated Au stralia, Commonwealth Scientific and Industrial Researc h values given by Hilsenrath [33]. Values of L ~ were ob Organization, National Standards Laboratory, Division of Physics. University Grounds, Sydney, Australia, July 1949. tained by linear interpolation from the tabulation in [5] Ivory, J. , On the hygrometer by evaporation, Philosophical the International Critical Table [35]. A value of unity Magazine 60, 81 (1822). was ascribed to fw and vapor pressures were calcu- [6] August, E. F. , Uber die VerdunstungskaIte und deren Anwen dung auf Hygrometrie, Ann. der Physik und Che mi e 5, 69 (1825). :J The saturation vapor pressure of a liquid substance in the presence of an in e rt gas [7] Apjohn, J. , Formula for inferring the dewpoint from indications diffe rs from tha t when the pure substa nce alone is present. The factor ! ". accounts for thi s of the wet·bulb hygrometer, Phil. Mag .. 6, 182 (1835). difference. It is defined as f tA P. T1· ) = ¥.~ where XI' is the mole frac tion of the vapor in a [8] Apjohn, J., On the theory of the moist bulb hygrometer, Trans. vapor·gas mixture under sa turation a l te mperature Tu' and lotal absolute pressure P. Roy. Irish Acad. 17, 275 (1837). 46 [9] Whipple, F. 1. W. , The wet and dry bulb hygrometer: The rela· [25] Carrier, W. H. and Lindsay, D. C., The te mperature of evap tion to theory of the experime ntal researc hes of Awberry oration of water into air, Trans. of Am. Soc. Mec h. Eng. 46, and Griffiths, Proc. Phys. Soc. London 45, 307 (1933). 739 (1924). [10] Carrier, W. H. , Rational psyc hrometric formulae, Am. Soc. [26] Harrison, L. P., Proposal for an Experimental Triple- tubed Mech. Engrs. Trans. 33, 1005 (1911). Adiabatic Saturator to Measure Thermodynamic Wet-Bulb [11] Arnold , J. H., The theory of the psyc hromete r. LI. The effect Temperature as a Limit Approached During the Saturation of veloc ity, Physics 4, 334 (Sept. 1933). Process, Humidity and Moisture 1, 33 (Reinhold Publishing [12] Sherwood, T. K. and Co mings, E. W. , On experimental study Corp., New York, 1965). of the wet·bulb hygrometer, Trans. Am. Inst. Chem. Eng. [27] Lewis, W. K. , The Evaporation of a Liquid into a Gas, Trans. 28, 88 (1932). Am. Soc. Mech. Engrs. 44, 325 (1922). [13] Lewi s, W. K., The evaporation of a liquid into a gas-a correc [28] Nanda, V. S. and Kapur, R. K., A note on the thermodynamics ti on, Mech. Eng. 1. 55, 567 (1933). of the wet- and dry· bulb hygrometer, Indian J . Phys. 31,391 [14] Dropkin, D., The Deviation of the Actual Wet-B ulb Te mpera (1948). ture from the Temperature of Adiabatic Saturation, Cornell [29] Wentzel, J. D. , An instrument for the measurement of the Univ e r sity Engineering Experiment Station, Bulletin No. 23 humidity of air, Ame rican Society of Heating, Refrigeration (July 1936). and Air Conditioning Engineers 10urnal 66, 67 (Nov. 1961). [1 5] Brun, E. and Lions, M., Sur la theori e gene rale du psychrometrie et sur une methode simple d'etude exp erime ntale des lois [30] Harrison, L. P., Fundamental Concepts and De finitions, Humid de diffusion wrcie , C. R.A. S. (Paris) 222, 1071 (1946). ity and Moisture 3, 3 (Reinhold Publishing Corp. , New York, [16] Kaw ata, S. and Omori Y., An investigation of thermocouple 1965). psychromete r I, J. Phys. Soc. Japan 8, No.6, 768 (1953). [31] Smithsonian Meteorological Tables, Smithsonian Institution, [1 7] Maxwell, 1. c., Diffu sion , Encyl. Brit. 9th Ed . VlI, 218 (1877). Washington, D. C. (1951). [18] Mi eghe m , J. Van, La Thermodynamique du Thermometre [32] Goff, 1. A. , Saturation Pressure of Water on the New Keivin Moui iJ e, Bull. Classe Sci. Acad. Roy. Belgi. Bruxilles 27,85 Scale, Humidity and Moisture 3 , 289 (Reinhold Publishing (1941 ). Corp., New York, 1965). [19] Svenn son, A. , Verdunstung und Abki.ihlung oder Erwarmung [33] Hil senrath, J. , et aI. , Tables of thermal prope rties of gases, in de m Laminaren Gasstrom von Konsta nter Geschwindig. NBS Circ. 564 (1955). ke il. Anwendung auf Assmansche Aspiration-psychromete r, [34] Bain , R. W., S team Tables, Department of Scientific and In· Arkiv_ f. Mat. Astron. oc h Ph ys ik. Stockholm , Hafte 4, 22A, dustrial Research, National Engin eering Laboratory, East 23 (1932). Kilbride, Scotland (1964). [20J Threlk eld, 1. L. , Thermal Envi ronme ntal Engineering, Pren ti ce·Hall, Inc., Englewood C liffs, N.J. (1962). [35] International Critical Tables (McGraw-Hili Book Co., Inc.,. [21] We ber, S., Psychrometrets Teori , Dans k Videnskobernes Sels k, New York , N.Y. , 1928). Mathem-fys. Medd 3, No . 19 (1921). [36] Hilde nbrand, D. L. and McDonald, R. A. The Heat of vaporiza· [22] Arnold , J . H., The theory of the ps yc hromete r. 1. The mech tion and vapor pressure of carbon tetrachloride; the e ntropy ani sm of evaporation , Phys ics 4, 255 (Jul y 1933). from calorimetric data, 1. Phys. Chem. 63, 1521 (1959). [23] Go ff, J. A., Standardization of thermodynamic properties of [37] Rossini , F. D. , et a I. , Valu es of Physical and The rmodynamic moist ai r - final report of working subcommittee, Inte rna Prope rties of Hydrocarbons and Related Compounds (Car· tional Joint Co mmittee on Psychrometric Data, ASHVE negie Press, Pittsburgh, Pa., 1953). Journa l Section, Heating, Piping and Air Conditioning 55, [38] Scott, D. W., et aI., Tolue ne thermodyna mi c properties, mol ec 118(1949). ular vibrations and internal rotation, J. Phys. Che m. 66, 911 [24] Go ff, 1. A. , and Gratch, S., The rmal prope rties of moist... air, (1962). AS HVE Journal Section, Heating, Piping and Air Condition in g 51,334 (June 1945). (Paper 72Cl-267)
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