A novel concept in the design of a psychrometer

Transcription

1 ndian Journal of Enineerin & Materials Sciences Vol. 1, December 005, pp A novel concept in the desin of a psychrometer Sunit Kumar Sen Department of Applied Physics, University Collee of Technoloy, University of Calcutta 9, APC Road, Calcutta , ndia Received 14 June 004; accepted 1 Auust 005 A novel psychrometric method for measurement of humidity of a process is proposed. The desin of a psychrometer is a complex one due to simultaneous introduction of two variables at the same time, viz., the meter current is dependent on both the relative humidity and ambient temperature. The circuit desin has been so made that the said current would depend only on the relative humidity of air and independent of temperature variations at the place of measurement. Theoretical calculations show that the maximum error in the measurement of the meter current would be limited to within +1.6% at 10 F and -% at 60 F for 100% relative humidity while the same would be within ±1.75% for the entire temperature rane F for 0% relative humidity. PC Code: G01N5/6 Measurement and control of humidity is of prime importance in several industrial and aricultural fields. For example, in textile mills, humidity has to be maintained at the exact level to ensure proper handlin of the yarn. Precision metal parts are affected by too much of humidity. Maintainin a proper humid environment is one of the essential criteria in pharmaceutical industries as also in bacterial rowth. The technique for the measurement of humidity is an old one 1,. Researchers tried to develop and improve upon the humidity sensors 3-5 to decrease errors in measurements of humidity. The technique of measurement in these capacitive type sensors is based on chane of capacitance in a linear manner with relative humidity. These are preferred because of accurate and stable measurements at room temperatures. Yan 6 ave an idea of the developments in this field. Of late diital techniques and hih accuracy circuits for on-chip capacitance ratio testin and sensor readout for humidity sensors were reported by researchers 7-9. Bucci et al. 10 utilized the piecewise linear characteristics of a new ADC for implementin a smart humidity sensor. Shi et al. 11 reported a simadelta (ΣΔ method of diital readout technique for a capacitance type humidity sensor. The proposed technique for measurement of humidity is based on the well-known Wheatstone s bride principle. The unbalance bride current is made to have a proportional relationship with humidity and independent of temperature variations of the sensor. The paper has dealt in details the proposed technique in circuit that has been adapted to make the meter current independent of temperature variations and ultimately went on establishin the maximum percentae error that may creep into under the most extreme conditions of humidity measurements. Standard Bride Circuit t is an application of Wheatstone s bride in the measurement of humidity of air by dry and wet bulb thermometers made of electrical resistances. Let us consider the Wheatstone s bride network as shown in Fi. 1. The unbalanced current throuh the detector G is iven by: ERR ( 3 RR 1 4 RR ( R1 + R + R3 + R4 + R ( R1 + R3( R + R4 + R ( R + R ( R + R + RR ( R + R + R R ( R + R (1 Assumin, R 3 R 4 R, R ar, R br Also, let R 1 R + ΔR 1 and R R + ΔR, where ΔR 1 and ΔR are the small variations of R 1 and R from the value of R at some reference temperature. Puttin these values in Eq. (1 and nelectin terms containin hiher orders in ΔR 1 and ΔR, is reduced to:

2 SEN: A NOVEL CONCEPT N THE DESGN OF A PSYCHROMETER 499 constant. Assumin constant values of K and E (supply voltae, the detector current becomes proportional to (ΔR - ΔR 1. Fi. 1 A standard Wheatstone s bride network Fi. Circuit diaram of the desined humidity meter E( ΔR ΔR 1 1( b+ 1 R + ( ab+ a+ b+ 3 R( Δ R1+ΔR E( ΔR ΔR 1 R + 4 b( a+ 1 R + R( ab+ a+ b+ 3( Δ R +ΔR 1 E( ΔR ΔR K 1 1 where, K 4(a+1 R + 4b(a+1 R + R(ab+a+b+3 (ΔR 1 +ΔR. f R and a are constants but b, ΔR 1 and ΔR are variables, the first term in the expression for K becomes constant, whereas the second and third terms are variables. However, by properly chanin the value of b with variations in ΔR 1 and ΔR, the second and third terms can be made practically constants and if this is possible then K becomes practically Description of the Desined Pshychrometer Fi. shows the circuit diaram of the desined humidity meter. The Wheatstone s bride circuit contains the dry bulb (D and the wet bulb (W thermometers made of copper resistances in the first and second arms respectively, toether with other resistances. The third and fourth arms contain mananin resistances, each of value R. The resistances of R t and R t also become equal to R at some reference temperature which for our case has been taken as 90 F. The total resistance in the first arm is into two parts-one is dry bulb, made of copper and of value (l-mr t, where m is the slope of the relative humidity line and R t is the value of the copper resistance at the temperature t. The other is made of mananin and of value mr. The situation is similar for the wet bulb in the second arm also, where R t is made of copper and r is made of mananin. At any temperature and relative humidity, the total resistance of the second arm is made reater than that of the first arm. Theory The desined humidity meter has a temperature and humidity rane of 60 F to 10 F and 0% to 100% respectively. Within this rane of ambient temperature and relative humidity, approximate straiht line raphs are obtained as shown in Fi. 3, courtesy, Cambride nstruments Co. Ltd, by plottin depression, i.e., (dry bulb temperature wet bulb temperature aainst ambient temperature (dry bulb temperature with relative humidity. One such curve is shown in Fi. 4 in which the variables alon the X and Y axes are swapped with respect to Fi. 3. Let δ be the depression at reference temperature (taken as 90 F for this particular relative humidity. f the ambient temperature increases by Δt, the depression for the same humidity will be (δ+mδt, where m is the slope of that relative humidity line. f both the dry bulb temperature t and the wet bulb temperature t are assumed to be reater than the reference temperature, then the resistances R t and R t are iven by: R t R(1+βΔt R t R(1+βΔt,

3 500 NDAN J. ENG. MATER. SC., DECEMBER 005 Fi. 3 Graphs of depression of wet bulb versus dry bulb temperature Fi. 4 Graph of dry bulb temperature versus depression where, Δt and Δt are the increments in the dry and wet bulb temperatures respectively, over the reference temperature and β is the resistance temperature coefficient of copper and referred to the reference temperature 90 o F. Since, Δt Δt (δ+mδt, where m is the slope of the relative humidity line correspondin to the relative humidity to be measured. We have, R t R [1+β{Δt - (δ+mδt}] We introduce a fraction (1-m of the total resistance into the first arm so that the effective dry bulb resistance is iven by: R D (1-m R t (1-m R (1+βΔt The mananin resistance put in series with the dry bulb in the first arm is of value mr. t is such that the total resistance of the first arm is equal to R for any value of m if the ambient temperature is equal to the reference temperature. Hence, the total resistance of the first arm at any ambient temperature t is iven by: R 1 R D + mr (1 - m R (1 + βδt + mr R + (1 m βrδt The total resistance of the second arm is iven by: R R w + r R t + r R [1 + β { Δt (δ + mδt}] + r Therefore, variation of R 1 from R is ΔR 1 (1 m βrδt and, variation of R from R is ΔR Rβ[Δt (δ + mδt] + r Therefore, ΔR - ΔR 1 r - Rβδ ( f is assumed to be proportional to (ΔR - ΔR 1, then K 1 (ΔR - ΔR 1 K 1 (r - Rβδ (3 where, K 1 is a constant of proportionality and is iven by, K 1 (E/K From Eq. (3, we see that is dependent only on δ, i.e., depression at the reference temperature for the particular relative humidity to be measured and is not influenced by ambient temperature. Thus, if we calibrate the detector current at the reference temperature in terms of the relative humidity, we can measure the relative humidity at other temperatures also, provided that the proper value of m is selected for the resistances in the first arm. Desin calculations The expression for is iven by: E( ΔR ΔR1 1 R assumin for the present that the second and third terms in the expression for K are neliible and replacin the value of (ΔR - ΔR 1 from Eq. (, we have, Er ( Rβδ 1 R (4

4 SEN: A NOVEL CONCEPT N THE DESGN OF A PSYCHROMETER 501 At the reference temperature 90 F, δ 0 for 100% relative humidity and δ38 F for 0% relative humidity. So as relative humidity chanes from 100% to 0%, the total variation in is then, ERβδ Eβδ Δ a+ R a+ R 4( 1 4( 1 (5 f we choose E4.5 V, R 00 Ω and β0.0015/ F, then, we have from Eq. (5, Δ 4(10 + 1( μ A (for a 10 The maximum value of Rβδ is Ω r should be reater than 16.7 Ω so that the microammeter deflection always remains in the same direction for any relative humidity for 0% to 100%. We choose, r 18 Ω So, we have, Er 1 R max and, Er ( Rβδ 1 R min (at 100% relative humidity (at 0% relative humidity By puttin the value of different quantities, max and min values were obtained to be 46 μa and 4.4 μa respectively. Thus, the above indicates the rane of the microammeter for the relative humidity rane from 0% to 100% Percentae error in K Since K is iven by K4(a+1R +4b(a+1R +(ab+a+b+3 R (ΔR 1 +ΔR 44R + 44bR + (3 +1b R (ΔR 1 +ΔR (6 (here, a 10, assumed At any ambient temperature and relative humidity, ΔR 1 (1-m RβΔt and, ΔR [Δt (δ + mδt] βr +r Therefore, ΔR 1 +ΔR (1 m βrδt + (r - Rβδ (7 Denotin the value of K at 90 F by K 90 and that at (90+Δt by K 90 + Δt for any particular relative humidity, we see from Eqs (6 and (7 K 90 + Δt K 90 (1 m(3 + 1b βr Δt (8 where, b is assumed to be a constant. Since the instrument is calibrated at 90 F, the error in K is to be calculated by takin K 90 as the correct value. The variation of K 90 with relative humidity is very small so that the percentae error is proportional to (K 90+ Δt K 90. From Eq. (8, we see that the percentae error is maximum when Δt is maximum and m0. Thus, the maximum percentae error in K occurs when relative humidity is 100% and ambient temperature is either 10 F or 60 F. Therefore, the maximum percentae error in K is: [(K 10 - K 90 /K 90 ] βr Δ t 100 (assumin, b 0 44R (3/ (since, Δt 30 F 6.7 The maximum % error in k will be 6.7 at 60 F and 100% relative humidity. Reduction in percentae error in K This is achieved by chanin the value of b with temperature. Let us assume that b 0 at 90 F for any relative humidity and as the temperature is chaned, some value of b is introduced. Thus, we can write. K 90 + Δt K 90 44bR + (1 m (3+1b βr Δt + 1bR (r - Rβδ 44bR + 46(1 m βr Δt This is put to zero for m 0.85 (m varies from 0 to 0.57 as relative humidity varies from 100% to 0%, which will enable us to find the rane of values of b for the entire rane of relative humidity just specified. Hence, we have, b - [(1 m 3 β/] Δt Δt Thus to compensate for the error in K when Δt 30 F (i.e., when the ambient temperature is 10 F and m 0.85, the value of b is to be decreased by an

5 50 NDAN J. ENG. MATER. SC., DECEMBER 005 amount Aain, when Δt -30 F (i.e., when the ambient temperature is 60 F, the value of b is to be increased by an amount of Since, b cannot be neative, we introduce an initial value b 0 of b equal to at 90 F. Thus, the required value of b at any ambient temperature is iven by the equation. b b Δt (9 Thus we see that the value of b is to increased or decreased from b 0 with decrease or increase of ambient temperature from 90 F to compensate for the error in K. At 10 F, B whereas, at 60 F, b For our convenience, we increase or decrease the value of b in steps of for each 10 F decrease or increase in ambient temperature from the reference temp 90 F. Since, R Rb and R 00 Ω, we have the value of R at 90 F to be equal to 9.64 Ω, at 10 F to be equal to zero and that 60 F to be equal to Ω. The steps for each 10 F variation in ambient temperature bein 3.14 Ω. Calculation of residual percentae error in the value of K Since K is corrected for m 0.85, we can uess that the maximum percentae error in K will occur when m 0 or 0.57 (i.e., relative humidity ranin from 100% to 0% and the ambient temperature is (90 ±10n ±5 F where, n0,1,. The value of b used bein that for (90 ± 10n F. To calculate the maximum percentae error, let us assume that m 0 (i.e., relative humidity 100% and ambient temperature (90±10n ±5 F, where, n 0,1, and the value of b used is b n Thus we can write, K (90 ± 10n ± 5 K 90 44(b 1 b 0 R + 46βR (±10n ±5 R (±0.819n ± (10 From Eq. (10, we see that the manitude of (K 90±10n ± 5 _ K 90 increases with n. Thus, at 115 F (with n and 65 F (with n -, it is maximum. We have (K 115 K 90 R and (K 65 K 90 -R So that the percentae error in K at 115 F is [(K 115 K 90 /K 90 ] 100 [ R /44R ] and that 65 F, it is The percentae error in the value of K will be of same manitudes at these ambient temperatures, but at the other extreme of relative humidity i.e., 0% for which m Thus, the maximum percentae error in K will be ±.4. Calculation of percentae error in relative humidity due to error in K The detector current is iven by K 1 (r - Rβδ Due to a.4% increase in K (at 115 F or 65 F, K 1 will be decreased rouhly by.343%, so that for the same value of relative humidity h 1, the detector current becomes K 1 ( (r - Rβδ K 1 (r - Rβδ Now, let K 1 (r -Rβδ, where δ is the depression at 90 F correspondin to another relative humidity h. Thus the percentae error in relative humidity will be [(h - h 1 /h 1 ] 100 (11 Now, from the above, we have, r - Rβδ (r - Rβδ or, δ 0.977δ (0.03r/Rβ ( /( F (1 Since, the.343% error in k occurs only at 100% and 0% relative humidities, we will calculate the % error in relative humidities for these values only. At 100% relative humidity, δ 0, so that from Eq. (1, we et δ F which corresponds to a relative humidity value of 96.15%. Hence, from Eq. (11 the percentae error in relative humidity will be 3.85%. At 90% relative humidity, percentae error is found to be less than 3%. Aain, at 0% relative humidity, δ 38 F, so that from Eq. (1, δ F. Hence, the

6 SEN: A NOVEL CONCEPT N THE DESGN OF A PSYCHROMETER 503 percentae error for 0% relative humidity case will be almost inconsequential. Thus, we see that the percentae error in the readin of the humidity meter due to the error in K is less than 4% and that too occurrin only at 100% relative humidity correspondin to an ambient temperature as low as 65 F or as hih as 115 F. The instrument will read correct value for 0% relative humidity and havin the same ambient temperatures of either 115 F or 65 F. Meter current t has been shown earlier that the meter current is representative of relative humidity, irrespective of temperature conditions. The meter current is iven by, Er ( Rβδ 1( b+ 1 R + ( ab+ a+ b+ 3 R[(1 m βrδ t+ ( r Rβδ] Er ( Rβδ 44R + 44 br + (3 + 1 b R[(1 m βrδ t+ ( r Rβδ] (by puttin a10 Assumin E 4.5 V, r 18 Ω, R 00 Ω, β / F and b is a variable as stated earlier. δ 0 at 100% relative humidity for the entire rane of temperature and δ38 F at 0% relative humidity for the same temperature rane. Aain, m0 for 100% relative humidity and m0.57 for 0% relative humidity. Puttin the appropriate values, the meter current was found to be μa, 41.3 μa and 4.81 μa at 90 F, 10 F and 60 F respectively with relative humidity assumed to be 100%. This amounts to a maximum percentae chane in meter current to be at 10 o F and.0 at 60 o F. f it is repeated for 0% relative humidity case, then the meter currents would be 4.03 μa, 4.11 μa and 3.96 μa at 90 F, 10 o F and 60 o F respectively. This thus amounts to a maximum percentae chane in meter current to be ± 1.74 either at 60 o F or 10 o F. Thus, it is seen that the meter current is solely dependent on relative humidity and independent of temperature the maximum meter current variation is limited to within ±% for 100% relative humidity with temperature varyin between the entire temperature rane considered, i.e., 60 to 10 F, while the same variation is limited to ±1.75% for 0% relative humidity for the same rane of temperature. Thus, it is seen that the meter current is almost remainin constant over the entire temperature rane considered, bein dependent only on relative humidity. Procedure to be adopted to measure relative humidity The resistance R (br in series with the battery is a variable mananin resistance of maximum value Ω. At 10 o F, value of R is zero and its value is increased by 3.14 Ω for every 10 F fall of temperature from 10 F. The dry bulb resistance and mananin resistance in series with it in the first arm are varied by a -pole 11-way switch (to account for eleven numbers of relative humidity values startin from 0% to 100% with a step size of 10% with each pole of the rotary switch touchin identical values of relative humidity positions of copper and mananin resistances, i.e., say touchin 10% relative humidity marked positions of copper resistance and 10% marked position of mananin. To determine the percentae relative humidity under any existin condition, we first note the ambient temperature and adjust the series resistance R accordinly. The selector switch is already calibrated in terms of percentae relative humidity startin from 0% to 100%. Now, we place the selector switch at any percentae position. f the actual value of relative humidity does not coincide with the relative humidity at which the switch is placed, the meter pointer would not show the actual value. So we o on adjustin the selector switch so that the meter pointer and the percentae relative humidity marked on the selector switch coincide. Thus the meter pointer position will ive us the relative humidity of the atmosphere. Conclusions The desin of the proposed humidity meter is based on the assumption that depression versus dry bulb temperature curves are straiht lines, which is a realistic one. n cases where extreme accuracy in the measurements is desired, piecewise linearization technique can be employed in which for a particular curve, very small differences in the values of m can be assined to overcome this drawback. The proposed psychrometric method of humidity measurement has totally eliminated one variable, viz., the dependence of humidity on temperature variations, makin the meter current a direct readin type for humidity measurements.

7 504 NDAN J. ENG. MATER. SC., DECEMBER 005 The proposed circuit for humidity measurement is a simple one, very easily implementable and the accuracy of measurement is dependent on the stability of the circuit components, viz., the resistances, which is not at all difficult to achieve. The desined instrument has taken into account the whole spectrum of relative humidity variations (viz., 0%-100%, but in actual practice where accurate measurement and control of relative humidity is necessitated, the rane required is very small. Hence, if the instrument is desined for a smaller rane of relative humidity measurements, percentae error in the measurement of relative humidity would have been much less. t is seen that at 100% relative humidity and a temperature of 115 F, the % error in the desined instrument is less than 4%. But 100% relative humidity is not frequently encountered in practice. At 90% relative humidity, the % error comes down to below 3% and the error reduces drastically with reduction in relative humidity ivin almost correct readin at 0% relative humidity. Thus, the desined humidity meter shows favourable results when compared with say Edetech s Model no. 645 which has an accuracy limit of ±1% between 10-90% relative humidity and ±% for the remainin rane. References 1 Wexler A, Ed, Humidity and Moisture, vol. 3, (Reinhold, New York Wexler A, Meteoroloical Monoraphs, 11 ( Schurser K, J Appl Phys, ( Thoma, P E, Colla, J O & Stewart, R A, EEE Trans Comput, Hybrids, Manufact Technol, CHMT- ( Schubelt P J & Nevin J H, EEE Trans Electron Devices, ED-3 ( Yan L C, Meas Control, 15 ( Shimizu H, Matsumoto H, Asakura M & Watanabe K, EEE Trans nstrum Meas, 37 ( Cao Y & Temes G C, EEE Trans Circuits Syst, 41 ( Wan B, Kajita T, Sun T & Temes G C, EEE Trans nstrum Meas, 47 ( Bucci G, Faccio M & Landi C, EEE Trans nstrum Meas, 49 ( Shi X, Matsumoto H & Murao K, EEE Trans nstrum Meas, 50 (