Robert R. Zarr

Thermal response simulation for tuning PID controllers in a 1016 mm guarded hot plate apparatus.

A mathematical model has been developed and used to simulate the controlled thermal performance of a large guarded hot-plate apparatus. This highly specialized apparatus comprises three interdependent components whose temperatures are closely controlled in order to measure the thermal conductivity of insulation materials. The simulation model was used to investigate control strategies and derive controller gain parameters that are directly transferable to the actual instrument. The simulations take orders-of-magnitude less time to carry out when compared to traditional tuning methods based on operating the actual apparatus. The control system consists primarily of a PC-based PID control algorithm that regulates the output voltage of programmable power amplifiers. Feedback parameters in the form of controller gains are required for the three heating circuits. An objective is to determine an improved set of gains that meet temperature control criteria for testing insulation materials of interest. The analytical model is based on aggregated thermal capacity representations of the primary components and includes the same control algorithm as used in the actual hot-plate apparatus. The model, accounting for both thermal characteristics and temperature control, was validated by comparisons with test data. The tuning methodology used with the simulation model is described and results are presented. The resulting control algorithm and gain parameters have been used in the actual apparatus without modification during several years of testing materials over wide ranges of thermal conductivity, thickness, and insulation resistance values.

Calibration of the NBS calibrated hot box

A series of calibration tests were conducted in the laboratory in order to determine the overall experimental error and uncertainty for the NBS calibrated hot box. For these tests, 10 cm (4 in.) and 20 cm (8 in.) thick polystyrene wall specimens having independently measured thermal resistances were installed in a support frame and sandwiched between the metering and climatic chambers. The metering chamber was operated at a typical indoor condition for a residence, while the climatic chamber was operated at selected steady outdoor winter conditions. For each of the tests, an energy balance was performed on the metering chamber. The heat transfer that flanks the wall specimen and passes through the support frame was predicted using a finite-difference model. The other heat losses and gains for the energy balance were measured. The residual energy loss for the energy balance of the metering chamber represents the overall experimental error and uncertainty. The maximum observed residual energy loss for all of the calibration tests without the metering chamber cooling coil operated was 1.9 W. This value occurred when the 10 cm (4 in.) wall specimen was exposed to a 23 K (41°F) temperature difference. This value, however, comprised only 1.8% of the net energy input to the metering chamber.

Assessment of Uncertainties for the NIST 1016 mm Guarded-Hot-Plate Apparatus: Extended Analysis for Low-Density Fibrous-Glass Thermal Insulation

An assessment of uncertainties for the National Institute of Standards and Technology (NIST) 1016 mm Guarded-Hot-Plate apparatus is presented. The uncertainties are reported in a format consistent with current NIST policy on the expression of measurement uncertainty. The report describes a procedure for determination of component uncertainties for thermal conductivity and thermal resistance for the apparatus under operation in either the double-sided or single-sided mode of operation. An extensive example for computation of uncertainties for the single-sided mode of operation is provided for a low-density fibrous-glass blanket thermal insulation. For this material, the relative expanded uncertainty for thermal resistance increases from 1 % for a thickness of 25.4 mm to 3 % for a thickness of 228.6 mm. Although these uncertainties have been developed for a particular insulation material, the procedure and, to a lesser extent, the results are applicable to other insulation materials measured at a mean temperature close to 297 K (23.9 °C, 75 °F). The analysis identifies dominant components of uncertainty and, thus, potential areas for future improvement in the measurement process. For the NIST 1016 mm Guarded-Hot-Plate apparatus, considerable improvement, especially at higher values of thermal resistance, may be realized by developing better control strategies for guarding that include better measurement techniques for the guard gap thermopile voltage and the temperature sensors.

A Dynamic Test Method for Determining Transfer Function Coefficients for a Wall Specimen Using a Calibrated Hot Box

This paper describes a dynamic test method for determining transfer function coefficients (TFCs) for a wall specimen using a calibrated hot box (CHB). In this method, a wall specimen is installed between the climatic and metering chambers of a CHB. After a steady specimen heat transfer rate is attained, the air temperature in the climatic chamber is quickly ramped from an initial to a final temperature level in a linear manner. The final temperature level is maintained until a new steady specimen heat transfer rate is attained. The metering chamber is maintained at a steady indoor condition and is used as a calorimeter. The transient heat transfer rate at the inside surface of the wall specimen is determined at hourly time steps from an energy balance of the metering chamber. The poles and residues for a ramp analytical solution are derived by analyzing the measured specimen heat transfer response. The ramp analytical solution is subsequently used to form a triangular pulse from which TFCs are derived. The dynamic test method was conducted on a masonry wall. Empirical TFCs derived by the test method predicted the diurnal performance of the wall specimen with good agreement. In fact, the results predicted by empirical TFCs tracked the measured results as closely as an analytical model.

Calibration of Thin Heat Flux Sensors for Building Applications Using ASTM C 1130

Calibration measurements of thin heat flux sensors for building applications are presented. The findings support the continued development of precision and bias statements for ASTM Practice C 1130. Measurements have been conducted using a 1016 mm diameter guarded hot plate apparatus (Test Method C 177) from 10°C to 50°C and for a heat flux range of ± 13 W/m2. The option of using a 610 mm heat flow meter apparatus (Test Method C 518) to calibrate the heat flux sensors is also explored. Experimental designs are presented to compare test methods, evaluate which parameters affect the sensor output, and determine the functional relationship between the sensor output and applied heat flux. The study investigates two sizes of sensors fabricated by one manufacturer. Sensor equivalency, grouped by size, is evaluated to determine whether a calibration based on a subset of sensors will suffice or if extensive individual calibrations are needed.

Interlaboratory “Pilot Run” Study of Small Heat-Flow-Meter Apparatus for ASTM C 518

Thermal conductivity measurements of a high-density glass-fiber thermal insulation material near 24°C are presented for the determination of the precision and bias of ASTM Test Method C 518. The measurements have been conducted by 13 laboratories using small (305 by 305-mm) heat-flow-meter apparatus on three specimens of high-density glass-fiber thermal insulation material that were circulated among the laboratories. Test results are analyzed using ASTM Practice E 691 and subsequently compared to measurements of the same specimens conducted in a guardedhot-plate apparatus using ASTM Test Method C 177. The 95% repeatability and reproducibility indexes for precision have been determined to be no worse than 1.1 and 4.0%, respectively. A method for estimating bias is presented.

Retrospective Analysis of NIST Standard Reference Material 1450, Fibrous Glass Board, for Thermal Insulation Measurements.

Thermal conductivity data acquired previously for the establishment of Standard Reference Material (SRM) 1450, Fibrous Glass Board, as well as subsequent renewals 1450a, 1450b, 1450c, and 1450d, are re-analyzed collectively and as individual data sets. Additional data sets for proto-1450 material lots are also included in the analysis. The data cover 36 years of activity by the National Institute of Standards and Technology (NIST) in developing and providing thermal insulation SRMs, specifically high-density molded fibrous-glass board, to the public. Collectively, the data sets cover two nominal thicknesses of 13 mm and 25 mm, bulk densities from 60 kg·m−3 to 180 kg·m−3, and mean temperatures from 100 K to 340 K. The analysis repetitively fits six models to the individual data sets. The most general form of the nested set of multilinear models used is given in the following equation: λ(ρ,T)=a0+a1ρ+a2T+a3T3+a4e−(T−a5a6)2where λ(ρ,T) is the predicted thermal conductivity (W·m−1·K−1), ρ is the bulk density (kg·m−3), T is the mean temperature (K) and ai (for i = 1, 2, … 6) are the regression coefficients. The least squares fit results for each model across all data sets are analyzed using both graphical and analytic techniques. The prevailing generic model for the majority of data sets is the bilinear model in ρ and T. λ(ρ,T)=a0+a1ρ+a2T One data set supports the inclusion of a cubic temperature term and two data sets with low-temperature data support the inclusion of an exponential term in T to improve the model predictions. Physical interpretations of the model function terms are described. Recommendations for future renewals of SRM 1450 are provided. An Addendum provides historical background on the origin of this SRM and the influence of the SRM on external measurement programs.

Expanded polystyrene board as a standard reference material for thermal resistance measurement systems

Thermal conductivity measurements at room temperature are presented as the basis for certified values of Standard Reference Material 1453, Expanded Polystyrene Board. The measurements have been conducted in accordance with a randomized full factorial experimental design of two variables, bulk density and temperature, using the National Institute of Standards and Technology one-meter line-heat-source guarded hot plate. Uncertainties of the measurements, consistent with current international guidelines, have been prepared. The thermal conductivity measurements were conducted over a range of bulk density of 37.4 to 45.8 kg/m 3 and mean temperature of 281 to 313 K. Statistical analyses of the physical properties of Standard Reference Material 1453 are presented and include variations between boards, as well as within board.

Control Stability of a Heat-Flow-Meter Apparatus:

Calibration measurements of a commercial heat-flow-meter appara tus are presented. The apparatus has been calibrated using the same specimen of high-density fibrous-glass board over a period of four years, from 1989 to 1993. Seventy-three tests have been conducted, generally at ambient conditions of 24°C with a moderate temperature difference of either 15, 22 or 27°C across the specimen. Variations within a set of data for each test have been examined to verify underlying assumptions of randomness, normal frequency distribution of errors, repeatability, and stability of the data. Variations between test data indicate a small drift, on the order of one percent over four years, in the calibration factor of the apparatus. A model has been developed to describe the small drift with time. The analysis of varia tions between test data has also identified intermittent shifts in the precision of the calibration factor of the apparatus.

Thermal Resistance Measurements of Well-Insulated and Superinsulated Residential Walls Using a Calibrated Hot Box:

Thermal resistance measurements of two highly insulated residential walls are made using a calibrated hot box operated under winter and summer climatic condi tions. The well-insulated wall consists of two insulated wood-frame sections with staggered framing, having a nominal thermal resistance of R-27 F·ft2·h/Btu (4.8 K· m2/W). The superinsulated wall is identical in construction, except for additional in sulation placed between the two wood-frame sections increasing the wall thermal re sistance to a nominal value of R-39 F·ft2·h/Btu (6.9 K·m2/W). The measured thermal resistance for both walls is examined as a function of mean wall temperature and compared with predictions using the ASHRAE parallel-path method, the ASHRAE isothermal-plane method, and a finite-difference model with temperature-dependent thermal conductivities. Good agreement between measured and predicted values is obtained using both ASHRAE methods and the finite- difference model. At mean wall temperatures above 40°F (4.4°C), the ASHRAE parallel-path method tends to overpredict, while the ASHRAE isothermal-plane method tends to underpredict the overall thermal resistance. The effects of the com pression of glass-fiber blanket insulation and nail penetrations on the overall thermal resistance are investigated.