1、_- International Journal of Heating,Ventilating, Air-conditioning and Refrigerating Research HVAC nor may any part of this book be repro- duced. stored in a remeval system. or transmitted in any form or by any means-electronic. photocopying. recording. or other -without permission in writing hm ASHR
2、AE. hats-Abstracted and indexed by Engineering Informa- tion. Inc. Available electronically on Compendex Plus and in print in Engineering Index. Dircliimer-ASHRAE has compiled this publication with care. but ASHRAE has not investigated. and ASHRAE expressly disclaims any duty to Investigate. any pro
3、duct, service. process. procedure, design, or the like which may be described herein. Ihe appearance of any technical data or editorial material in this publication does not constitute endorsement. warranty. or guaranty by ASHRAE of any product, service. process. proce- dure. design, or the health a
4、nd comfort (9%); buildings, energy (22%); air and hydronic equipment, boilers (5%); fundamentals, heat transfer, fluid flow (25%); controls (15%). Analysis of this data gave us some surprises. For example, we had expected more manuscripts in the equipment, buildings and controls areas than the other
5、s, but had not expected that the greatest number of manuscripts would be in the fundamentals area. In retrospect, this distribution is understandable, since our focus is on research. In my first editorial, I reported that our associate editors indicated four research areas that they thought containe
6、d hot research topics.” The manuscripts published fit these Categories in the following way: Ozone and global warming (38OhI; Application of new control science (14%); Human comfort and indoor air quality (12%); New methods of analysis and/or experimentation (26%); Other (10%). Authors submitted man
7、uscripts from the following countries: Canada, France, Ger- many, Hong Kong, India, Ireland, Israel, Italy, Japan, Kuwait, New Zealand, Peoples Republic of China, Puerto Rico, Saudi Arabia, Singapore, Spain, Sweden, Switzerland, Taiwan, The Netherlands, Turkey, the United Kingdom, United States. It
8、is pleasing to note that we had manuscripts from so many different countries. Two-thirds of the sub- missions came from the United States, and one-third from the other 22 countries, sup- porting our belief in substantial world wide interest. The improvement in the acceptance rate of manuscripts over
9、 the initial statistics indi- cates that our focus on archival research papers is becoming understood. In the begin- ning, the rate of acceptance was very low, due no doubt to the research objectives of HVAC and a = 1.5 for tall, narrow buildings. They suggest that this is the result of high initial
10、 shear and turbulence, and the three-dimensional obstacle-gen- erated vortices that are not included in Hunts far-wake theory. For simplicity our wind shadow wake used a single value of a = 1.5. Speed Reduction in the Wind Shadow The magnitude of the shelter factor was found by applying measured win
11、d pressure coefficients to the functional form of wake decay discussed in the previous section. The velocity in the notch wake is the velocity required to obtain the correct surface pressures. In the most common cases shelter is provided by obstacles closer than three building heights away. To accou
12、nt for initial wake width, a virtual origin displacement was intro- duced by rewriting Equation (8) as where BI and then a new model using the van der Waals (vdW) equation is discussed. Detailed procedures for setting up the constants for the EOS are described. The actual applications of the model a
13、re shown, using pure R-32 and R- 125 and their binary mixtures. CUBIC EQUATIONS OF STATE Familiar cubic EOS may be written in a general form as: RT a p= - V- b V2+ mbV+ nb2 The (cubic) polynomial form in volume is expressed as: (2) 3 nbLRT ab PP V-nb -=O Commonly known equations are obtained by sett
14、ing rn = O, n = O (vdw): rn = 1. n = O (RK and SFW); rn = 2, n = -1 (PR), respectively. Several approaches have been used to set the values of the two parameters, a and b, that appear in Equation (1). For pure compounds, the critical point conditions are often applied by retaining T, and P, and igno
15、ring V, and then the parameters a and/or b are treated as arbitrary functions of T. For mixtures, the following mixing rules for the parameters a and b are usually adopted with empirical adjustable parameters kg and rq,. which are often called binary interaction parameters. a = 5 fij( 1 - ku)xixj Lj
16、= 1 b,+ b. b= +(1 - rnU)xixj i,j= 1 No single cubic equation of state can provide precise descriptions of real-fluid behav- ior, except over limited ranges of the state variables. An improvement for the cubic Equation (1) has been made by Carnahan and Starling (1972). replacing the first term in Equ
17、ation (1) by: RlY64V3+ 16bV2+4b2V- b3 V( 4 V - b)- (4) The earlier CSD EOS in NIST (1993) is this type of equation. The volumetric pro- perties in the liquid state have been significantly improved, but it is still a two parame- ter (a and b) EOS and there are serious problems at high temperatures in
18、 property calculations such as for latent heat of vaporization (Osajima et al. 1994). Although the familiar cubic equations are only for limited application ranges, proper use, with a few modifications, will provide sufficient accuracy in thermodynamic prop- erties and relations. One of the unique c
19、haracteristics of mixtures, and different from pure compounds, is the VLE (vapor-liquid-equilibrium) behavior. VLE calculations with EOS are complex and require tedious iterative computations. The cubic equations are not only simpler to use, but also it is known that the pressure-temperature-composi
20、tion 286 HVAC while real fluid values lie in the range from 0.2 to 0.3. Thus, the volumetric properties will suffer serious problems near the critical point. An obvious thought would be to introduce a third parameter to satisfy the three constants T, Pc and V, and the earliest attempt at this proced
21、ure was made by Clausius (1880): RT a p=- V-b (V+C) (5) In fact, Martin (1979) concludes that the Clausius-type equation is the best of the sim- pler cubic equations for presentation of volumetric data of pure fluids. In the present study, however, we introduced the third parameter as a linear trans
22、- formation of V (V = u + c) into the commonly known equations, since in this way we could still use all thermodynamic relations of those equations and existing computer programs without alterations. This was first examined using the SRK equation. Later we found that any common cubic equation worked
23、 equally well, with the same accuracy for the property calculations. Therefore, the simplest equation among them was chosen. With V = u + c, this becomes the familiar van der Waals form: RT a V-b V2 p= (7) Here, c is a constant for each pure compound, and since the differential dV = du, all thermody
24、namic relations can be constructed by the van der Waals Equation (7). Also, for simplicity, the parameter b is assumed to be a constant for each pure compound and only the parameter a will be an empirical function of T. The mixing rule for mix- tures is the usual one mentioned before, except for the
25、 specific forms of T-dependent functions. Then, for a general N-component system, the three parameters a, b, and c are modeled by: ASHRAE TITLE*IJHVAC 2-4 96 0759650 0525434 23T VOLUME 2. NUMBER 4. ocrOBER1996 287 N a = 2 Gj( 1 - kU)xiXj ij= 1 27 (RTcil2 a . = - CI 64 P, a, = aciai(T), 2 k = AU+BUT+
26、CUT, k= JI k y k= II O Y bi+ b. b = -2J( i - rny)xixj, qj = 9, , mi, = 0 i,j= 1 N c = c cixi i= 1 (81 (14) These are the general equations used in the present study. The constants that appear in these equations must be determined from experimental data, which is discussed in the next section. DETERM
27、INATION OF EMPIRICAL CONSTANTS Because the mixture EOS is based on each pure component EOS through the mixing rules, the pure compound EOS must first be modeled accurately. Furthermore, as men- tioned earlier, we separately modeled the superheated vapor, two-phase WE) and com- pressed liquid states
28、in order to overcome limitations of the cubic-type equation. Superheated Vapor Equations (Vapor-EOS) For each pure component, the five constants k (k = O to 4) in Equation (10) and c in Equation (14), must be determined from experimental PiT data (pressure, volume, temperature). However, data with d
29、ensities larger than 0, or smaller than V, which are in the range of liquid-like supercritical fluid, should not be used. This is because no cubic equation can fit them simultaneously with low density data, and much higher-order terms in volume are required to model such regions. This modeling is be
30、yond the scope of the present work, although a high density compressed liquid region will be presented in a later section. VLE Equations WEEOS) The two-phase region is governed by the VLE conditions. The proper thermodynamic relations must be satisfied. Here, we treat volume or density) merely as an
31、 intermedi- ate variable; that is to say, we dont care whether Vis a really correct value or not. This does not violate thermodynamic principles. At a given T, P is uniquely determined at the VLE state, and then V is simply determined as roots of the cubic EOS. In fact, V ASHRAE TITLEaIJHVAC 2-4 96
32、m 0759650 0525435 176 m 288 WAC- RESEARCH acts literally as an intermediate variable, and the VLE condition is essentially the ther- modynamic relationship between T and P. Therefore, the parameter c in Equations (6) and (14) can be simply set to zero. Actual values for V (or density) can be obtaine
33、d from different methods when they are needed: saturated vapor V from the Vapor-EOS and saturated liquid V from the method described in the later section titled Liquid. What we are concerned with here is the precise presentation of the vapor pressure relation (P versus TI, enthalpy H, and entropy S,
34、 and reasonably accurate heat capacities and speed of sound at the saturated state. First, the empirical constants in a(T), which are k (k = O to 3) in Equation (10). were determined using vapor pressure data from the following thermodynamic VLE condition: This is the basis of the familiar Maxwells
35、“equal-area“ construction for pure compound VLE. Explicitly in the present case, it became: From this equation at given T and P, the T-dependence in the a parameter, a(T), is uniquely determined at each data point, while Vu and V, satis Equation (7). Then. the k in Equation (10) can simply determine
36、d. Ordinarily, this is sufficient to calculate other thermodynamic properties such as H, S, Cu, Cp etc., using the equation of state and the thermodynamic derivative relationship, and it was also true for the Vapor-EOS case, where V was precisely fitted to the experimental data, as well as T and P.
37、Here, however, V is not used to fit any experimental data, and whole VLE conditions are imposed upon the parameter a i.e., a(?) through the arbitrary T-dependent function. There is no guarantee that the arbitrary function is the correct form and that its derivatives with respect to Tare correct and
38、accurate. In fact, we have found that many forms of Tfunctions can fit experimental vapor pressure data equally well. When a high accuracy such as less than 1% error is desired for these derivative properties, some special considerations are needed. We determine the 1st derivative of a(?) from exper
39、i- mental data or other reliable correlation, instead of taking the algebraic derivatives of a(7). A convenient way to do so is to use the latent heat of vaporization (or latent S). In the present model, S becomes a particularly simple equation: Here, a(T) implies da(T)/dT, but is not the algebraic
40、derivative of aT) above. It is determined from the above equation with the following empirical function of T. n= O ASHRAE TITLErIJHVAC 2-4 96 m 0759650 05254Lb O02 m VOLUME 2. NUMBER 4. OCTOBER1996 289 Thus, the latent heat of vaporization (or latent S) can be correctly modeled. The next step is to
41、make sure absolute“ values in Hand S correct. We do this using the reliable correlation of St (and/or Hi) such as the MBWR as mentioned earlier. In the present model S!, measured from a reference state with So at To and Po, is: The integral of the ideal-gas heat capacity (Ci) enters the equation, be
42、cause we use the residual property to calculate the thermodynamic state in the usual fashion. The residual property is the deviation from an imaginary state, where the equation of state follows the ideal gas law (PV= RT), but it possesses real gas (non-interacting molecules) heat capacity Ci. Now th
43、at a(T) and a(T ) have been determined, the only adjustable parameter left is this integral term. This adjustment is allowed without violating any thermodynamic principle. Cpis usually treated as an empirical function of T anyway, and we could use a somewhat different one from the “real“ CP(T ) for
44、the above imagi- nary state, especially for VLE and liquid state calculations, while the “real“ Ci is used for the superheated vapor state. This seemingly inconsistent treatment may be resolved by considering the way to calculate the residual properties for VLE/liquid states, where all residual quan
45、tities require integration over the non-physical and artificial part of EOS: the so-called S“-loop (or van der Waals loop). Usually, we assume the analytical function including its derivatives to be valid inside the non-physical loop. It would be more natural to think of some corrections for this in
46、tegration procedure. Thus, the O present modification of the real ideal gas Cp can be regarded as such correction terms to the “real“ Cp . At any rate, we retain the same function form of T as the usual Ci for the VLE, but with different constant coefficients: O Co P = Co+ CIT+ C2?+ C3T3 These coeff
47、icients are determined from Equation (19) to fit Sl and/or Hl using the prede- termined a(T) and a( T ) . For mixtures, simply the molar fraction average of each pure compound will be used in the usual way. The saturated vapor properties calculated from VLE-EOS can be checked with those from Vapor-E
48、OS at the saturation dew point. In actual cases (see later sections). they agree within 1%. Thus, all saturated vapor properties can be calculated by Vapor-EOS. The main purpose in the present section was to obtain the correct and accurate satu- rated liquid properties. Finally, as for the second de
49、rivative properties (heat capacities and speed of sound), Vapor-EOS are used for the saturated and superheated vapor in the ordinaq thermo- dynamic relationships, while the liquid properties need some extra treatments and will be discussed in a later section. Mixtures Once the pure component EOS constants have been set, the necessary parameters for binary mixtures (kg and 5) in Equations (1 1) and (12) must be determined. For Vapor-EOS, PVT data of binary mixtures with different compositions are used, while for VLE-EOS, vapor pressure data with several d
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