Modeling snow melting on heated pavement surfaces. Part II: Experimental validation

Transcription

1 Applied Thermal Engineering 27 (27) Modeling snow melting on heated pavement surfaces. Part II: Experimental validation Xiaobing Liu a, Simon J. Rees b, Jeffrey D. Spitler c, * a Climatemaster Inc., 73 SW th Street, Oklahoma City, OK 73179, United States b Institute of Energy and Sustainable Development, De Montfort University, Queens Building, The Gateway, Leicester, LE1 9BH, United Kingdom c School of Mechanical and Aerospace Engineering, Oklahoma State University, 21 Engineering North, Stillwater, OK 77, United States Received 21 February 25; accepted 6 July 26 Available online 12 October 26 Abstract This paper describes an experimental validation exercise for a newly developed numerical model of the snow melting process on heated pavement surfaces. The model is able to predict the conditions of the snow, ice and water during the snow melting process on hydronically-heated pavements given time-varying weather and heating system boundary conditions. Validation results show that the model satisfactorily predicts the surface temperature and conditions, the degree of snow cover over the heated surface, and outlet fluid temperature given the weather data, inlet fluid temperature, and the fluid mass flow rate. It can therefore be used to analyze the performance of hydronic snow melting systems and can be used in the system design process. Development of the model is described in a companion paper. Ó 26 Elsevier Ltd. All rights reserved. Keywords: Experimental validation; Snow melting 1. Introduction * Corresponding author. Tel.: ; fax: address: spitler@okstate.edu (J.D. Spitler). Using an hydronic-heating system embedded in a pavement slab to prevent snow accumulation and ice formation on its surface has been proposed as an alternative to applying salt. In order to design a reliable and economically feasible hydronic snow melting system, it is desirable to evaluate various system designs under realistic weather conditions, which necessities the computer simulation of hydronic snow melting systems. A model that can accurately predict the performance of this snow melting system is the most crucial part of the simulation. Since it is usually necessary to examine the snow melting performance over a multi-year period, computational efficiency is also an important requirement for this model. A number of models of snow melting on hydronicallyheated pavements have been previously developed. However, they are either too simple to accurately predict transient and two-dimensional snow melting process [1 ] or can not quantify the snow conditions or degree of cover [5,6] and may be very computationally demanding [7]. Given system heat flux (or fluid temperature of the hydronic heating system) and weather data, the model studied here can predict the snow conditions and temperatures over the heated surface including the degree of snow cover (the proportion of the surface that is snow free). An intermodel comparison [] between this and a similar but more sophisticated model [7] has shown similar performance but with the advantage of significantly reduced computational demand. In order to further assess the validity of this model in simulating the performance of hydronic snow melting systems, experimental validation has been conducted using measured data taken from a full scale hydronically-heated bridge deck operated in real snowstorm conditions. A further review of literature and a complete description of the model are given in a companion paper [9]. In this /$ - see front matter Ó 26 Elsevier Ltd. All rights reserved. doi:1.116/j.applthermaleng

2 1126 X. Liu et al. / Applied Thermal Engineering 27 (27) paper, validation of this model using experimental data from a hydronically-heated bridge deck during a typical snowstorm will be presented. 2. Experimental snow melting system An experimental hydronic bridge snow melting system has been built at Oklahoma State University [1]. It provides a means of collecting experimental data for the purposes of model validation under various operating conditions. The experimental bridge deck is 1.3 m in length and 6.1 m in width (2 lanes wide). The embedded hydronic tubing is 19 mm diameter cross-linked polyethylene pipe on.3 m centers at a depth of 9 mm. An aqueous solution of propylene glycol at 39% concentration by mass is used as the heat carrier fluid circulated in the embedded pipe network. A ground coupled heat pump system was used to heat the propylene glycol solution and the maximum possible entering fluid temperature to the bridge deck hydronic heating system is about 5 C. The heating system is controlled to maintain the average bridge surface temperature at. C when there is a risk of icing or snowfall. Sixty thermistors are embedded at different locations in the pavement slab to measure the pipe wall and pavement surface temperatures. In addition, the leaving and entering fluid temperatures and the volume flow rate are measured with thermistor probes and flow meter, respectively. The estimated uncertainties of the temperature and flow rate measurements are ±.1 C and ±3%, respectively. Surface conditions are often considered in design calculations in terms of the fraction of the surface that is clear of snow. This is commonly denoted snow free area ratio or A r [11]. Hence, a snow free condition is indicated by a snow free area ratio of one, and a snow-covered surface as a value of zero. Patches of snow between pipe locations (striping) correspond to intermediate values. In this experimental work, this snow free area ratio has been estimated by examining images of the bridge surface taken during the snow event by a digital video system Model data The weather data used for the validation, except the snowfall rate, are obtained from the Oklahoma Mesonet, which is a network of weather stations throughout Oklahoma [12]. The local Mesonet weather station is approximately 1.6 km from the experimental bridge site. Measurements of precipitation at the bridge site were made with a heated tipping bucket rain gauge. This instrument was calibrated and the uncertainty found to be ±1%. Rather than using a model to calculate sky temperature, it has been measured directly at the bridge using a Kipp & Zonen CNR 1 four-component net radiometer. These data have been used as an input to the model during the validation exercise to eliminate one source of uncertainty. Comparison of sky temperature models has been reported by Liu [13]. Preliminary studies with this model showed some sensitivity to the thermal properties of the reinforced concrete substructure. The most appropriate values were found to be those calculated as a weighted average value of the concrete and steel reinforcement and according to the moisture content of the concrete. The effective pavement thermal properties at saturated condition are used in the following validation exercise since the snowfall during the simulated snow event was preceded by 3 h of rainfall (see Fig. ). Values of solar absorptance have been taken as.2 for a dry snow surface as suggested in CECW-EH [1]. For wet surface conditions the value is taken to be.5 1 as suggested by Levinson and Akbari [15]. Values for slush conditions are interpolated between these values based upon the mass of ice crystals in the slush layer Results In designing and evaluating snow melting performance, it is the calculation of surface temperatures and surface conditions (indicated by snow free area ratio) at any given time that is of prime concern. (System performance is often defined in terms of the number of hours the surface can be kept clear of snow vs. total hours of snowfall.) The ability to predict surface temperatures is not only of direct relevance to prediction of surface conditions, but is also of interest if one is concerned with modeling the whole heating system and its control systems. Similarly, heating system fluid temperatures/fluxes are of interest if the whole system is to be modeled and energy efficiency considered. Accordingly, it is the prediction of snow free area ratio surface and fluid temperature that are examined in evaluating the model. The validation exercise has been conducted by providing weather data, entering fluid temperature, and flow rate as inputs to the model and comparing the predicted average bridge surface temperature, exiting fluid temperature, and the degree of snow cover with the corresponding measured values. The data used were recorded during the snowstorm event on December 23, 22, which is representative of a heavy snowstorm. Besides the initial dry condition, four different surface conditions occur. The precipitation and surface conditions are indicated in Fig.. 1. Wet: rainfall from 6 a.m. for 3 h, surface above freezing temperature. 2. Slush and snow: complete snow cover for h. The heating system is started after 1 h. 3. Wet, slush, and slush and snow: various conditions as stripes appear during partial snow clearance.. Wet: snow clear but surface wetted by melt water. 1 Levinson and Akbari [15] suggested a.23 increase to the solar absorptance of a dry concrete surface to approximate the solar absorptance of the surface when it is wet.

3 X. Liu et al. / Applied Thermal Engineering 27 (27) Surface Temperature [ C] Dry Maximum (over a pipe) Average Wet Minimum (between two pipes From Slush to Wet, Slush, Snow + Slush Snow + Slush Start heating Begin striping Wet (with residual water) -2 12/23/2 : 12/23/2 6: 12/23/2 12: 12/23/2 1: 12/2/2 : Fig. 1. Variation of the calculated maximum, average, and minimum temperature at the pavement surface. Fig. 1 shows predictions of surface temperature during the storm. The temperatures shown are those calculated at positions directly above the heated pipe, and exactly midway between the pipes. As shown in the figure, the surface temperature remains at C at the point midway between the pipes before the entire surface is clear of snow and becomes wet. The maximum surface temperature occurs directly above the pipe location and rises quickly the average being correspondingly between these limits. Experimental data are not shown in this figure since surface temperatures were measured 1 mm below the surface in practice. Further comparisons are made using the temperatures calculated at the corresponding depth Surface temperatures Measured and predicted bridge average surface temperatures during the snow event are compared in Fig. 2. Precipitation type and surface conditions during the storm are also indicated on this figure. The average surface temperature drops immediately from approximately 2. C at the beginning of snowfall and remains at about.7 C until the heating system is started at 1: a.m. From this time, the bridge average surface temperature rises slightly as heat fluxes from the pipes increase. Although no snow free areas (striping) are detected, melting starts from the lower surface of the snow layer during this period. These temperatures appear slightly above freezing point as the sensors are slightly below the top surface, as noted above, and heat fluxes are upwards. Snow starts to clear from the surface at approximately 12.3 p.m. This is illustrated in the first of the images shown in Fig. 3 taken at 12.3 p.m when the snow free area is estimated as.5 (5% of the surface clear). Average temperatures then rise as part of the surface is cleared of snow the average temperature being that of portions of wet, slush and snow-covered regions. As more snow clears the rate of average surface temperature rise increases. Snow is found to have cleared completely at approximately 5 p.m. The difference between the predicted and measured average surface temperature varies according to the various surface conditions and so with the heat balance formulation applied in the model as described in [9]. It can be said that predicted temperatures vary in the same way as shown in the measurements as conditions vary, as indicated in Fig. 2. During initial dry condition (in the night), the surface temperature is determined by the balance between the convective and longwave radiative heat fluxes on the surface. Differences between measured and predicted surface temperatures are.7 C 2 in this period. Uncertainties of relevance in the modeling of these conditions are the values of surface properties and convection coefficients. Experimental uncertainties of concern are the measurement of surface temperatures and weather conditions. Of the weather conditions, the local wind speed is most likely to vary from measurements at the weather station. Previous measurements of surface properties and sky temperatures limit the uncertainty in radiant fluxes so that the chief concern is the uncertainty of the convective fluxes. Calculation of convective fluxes may be in error due the limitations of the applicability of correlations derived for flat plates to the bridge geometry (the bridge is significantly exposed on three sides). Differences between predicted and measured temperatures in dry conditions are discussed further in [13]. Differences in surface temperature predictions during wet conditions are limited to.2 C. In this wet condition, the surface is driven close to the ambient temperature because of the direct contact of the rainfall, which is 2 Differences between measured and predicted temperatures are RMS values over the period discussed.

4 112 X. Liu et al. / Applied Thermal Engineering 27 (27) Average Surface Temperature [ C] Dry Measured Predicted Wet From Slush to Wet, Slush, Snow + Slush Snow + Slush Start heating Begin striping Wet (with residual water) 12/23/2 : 12/23/2 6: 12/23/2 12: 12/23/2 1: 12/2/2 : Fig. 2. Comparison of measured and predicted bridge average surface temperature. Surface temperatures shown are from sensors 1 mm below the top surface and at corresponding points in the model. Fig. 3. Images of bridge surface condition taken by a digital camera along with estimates of snow free area ratio. The last image shows drifted snow on the heated surface after snowfall. assumed to be at the ambient temperature. The model represents this condition very well as uncertainties in surface temperature measurement are of the same order i.e., ±.2 C.

5 X. Liu et al. / Applied Thermal Engineering 27 (27) Dry Wet From Slush to Wet, Slush, Wet (with Snow + Slush Snow + Slush residual water) Start heating Begin striping Measured snow 2 free area ratio 16 Predicted snow -.2 Rainfall Snowfall free area ratio Precipitation -.6 Rate /23/2 : 12/23/2 6: 12/23/2 12: 12/23/2 1: 12/2/2 : Snow Free Area Ratio [-] Precipitation Rate [mm (equivalent water) / hour] Fig.. Comparison of measured and predicted snow free area ratio along with the precipitation rate. At the beginning of snowfall, the surface was observed to be in the slush condition because the snowflakes falling on the bridge were saturated immediately with the residual water (from previous rainfall) on the bridge surface. As the mass balance of water is not included in the model, the sensible heat of water is not taken into account in the simulation. This may account for the drop in temperature predicted at the start of snowfall being more rapid than that measured, and the average surface temperature being.5 C lower than measured data. These errors become less significant as snow melting progresses. As melting has progressed, stripes appear and the measured and predicted snow free area ratio increases until snow clearance is achieved. Surface temperatures are over-predicted and differences increase to. C. In addition to the noted uncertainties in the value of convection coefficients, the most significant experimental uncertainty is in the measurement of snowfall rate, which is estimated as ±1%. The effects of this uncertainty are discussed in the following section. Surface temperatures are also overpredicted in the later period when the surface is clear of all ice but remains wet. Differences between measured and predicted average surface temperatures increase to 1.5 C. This may be due to the assumption used in the model that there is no water on the surface after all the ice has been melted. Whereas, evaporation of water that is staying on the surface or penetrated into the pavement will in fact absorb some heat from the slab. Furthermore, it has been observed that some snow drifted from unheated surrounding regions to the heated portion of the bridge deck (see Fig. 3). It may also result in lower surface temperature because of melting this additional drifted snow, which obviously is not accounted for in the model Surface conditions Fig. 3 shows some of the digital images of the bridge surface during the snow melting process from which snow free area ratios (A r ) have been estimated. The variation of snow free area ratio during the snow event is shown in Fig. along with the rate of precipitation. It has been noted above that during the initial hour of snowfall the surface temperatures drop quickly and some melting occurs as the pavement top surface is initially above freezing point. As the rate of precipitation rapidly increases the surface becomes completely snow-covered (A r = ). The model provides indications of surface condition by various flags shown in the output. This, in addition to the trends in surface temperature and snow free area ratio, shows that the correct sequence of changes in surface condition are predicted: the sequence of conditions being dry; wet; slush; snow and slush; partial clearance; complete snow clearance. The model is limited in its ability to predict the final wet condition (after melting but without rain) due to neglecting the water staying on the surface and penetrated into the slab this has been noted previously. One of the prime concerns, when using the model to study safety and control of the system, is the onset and completion of snow clearance. This is indicated by the snow free area ratio raising above. and progressing towards 1.. The results shown in Figs. 3 and show that the onset of snow cover and start of snow clearance (striping) are matched to the measurements to within half an hour. 3 Predictions of snow free area ratio are very close to those measured in the range..5. There are more noticeable differences in the range.5 1. so that the final point of snow clearance is predicted one and half an hour later than that was observed. In the prediction of surface conditions, the main experimental uncertainty is in the measurement of snowfall rate 3 The values from the calculations do not change smoothly as there are a modest number of cells across the surface (1) and it may require a number of time steps before certain cells become snow free. The proportion of snow free cells consequently does not change smoothly.

6 113 X. Liu et al. / Applied Thermal Engineering 27 (27) From Slush to Wet, Slush, Wet (with 1. Dry Wet Snow + Slush Snow + Slush residual water) Start Begin 12 Measured average heating striping. surface temp..6 1 Results after - 1%. snowfall.2 Measured snow free area ratio Results after + 1% snowfall /23/2 : 12/23/2 6: 12/23/2 12: 12/23/2 1: 12/2/2 : Average Surface Temperature [ C] Fig. 5. Effect of snowfall rate on the model predictions of snow free area ratio and average surface temperature. Snow Free Area Ratio [--] as the accuracy of the heated tipping bucket gauge is limited to ±1%. Fig. 5 shows a sensitivity analysis with the snowfall rates 1% higher and 1% lower than that were recorded. Increasing the snowfall rate by 1% will reduce the discrepancies between the predicted and measured average surface temperature by.5 C but also result in about one more hour time lag in predicting the variation of snow free area ratio. Decreasing the snowfall rate by 1% has the effect of more accurately predicting complete snow clearance but bringing forward the predicted start of snow clearance. The rate of snow clearance is very similar in each case. This can be expected since this is essentially limited, at this point in the storm, by the heat input to the bridge. It is reasonable to say then that the predictions of snow free area ratio fall within the bounds of experimental error. The accuracy shown would be satisfactory for system design and performance evaluation tasks Fluid temperature The model has been implemented so that the heat source is specified in terms of a specified fluid inlet temperature and mass flow rate. This is the most convenient formulation for the simulation of the whole hydronic system along with the heated bridge deck. Since the heat delivered to the slab is indicated by the difference between the inlet and outlet fluid temperature, it is consequently important to validate the calculated outlet fluid temperature. Fig. 6 shows the comparison between the predicted and measured outlet fluid temperatures. The inlet fluid temperature is also included in the figure to indicate the overall Fluid Temperature [ C] 6 Bridge is Bridge is 55 Bridge is NOT Bridge is heated heated heated 5 heated continuously intermittently continuously 5 35 Measured inlet temperature 3 Measured outlet 25 temperature 2 Predicted outlet 15 temperature /23/2 : 12/23/2 6: 12/23/2 12: 12/23/2 1: 12/2/2 : Fig. 6. Comparison between measured and predicted bridge exiting fluid temperature.

7 X. Liu et al. / Applied Thermal Engineering 27 (27) temperature difference. The control system is designed to maintain the average bridge surface temperature at. C during the storm. The system output is modulated by switching the heat pump on and off intermittently. The intermittent operation of the system can be observed in this figure at the point where the surface is completely snow clear and surface temperatures rise. Fig. 6 demonstrates that the predicted outlet fluid temperatures match the measured data satisfactorily, except for some discrepancies at the beginning of the heating operation. The discrepancies are thought due to the coarse approximation of the round tube by the rectangular grid system applied in the finite difference computation domain. The RMS error during the entire heating operation is. C. Given the difference between the inlet and outlet temperatures during the heating operation is approximately 1 C, this corresponds to % over-prediction of the overall heat transfer. 3. Conclusion and recommendations A validation exercise using measured data from a full scale hydronically-heated bridge has been conducted to assess the validity of a pavement snow melting system model. Validation results show that this model satisfactorily predicts the surface temperature and conditions, the degree of snow cover over the heated surface, and the outlet fluid temperature given real transient weather data, inlet fluid temperature, and the fluid mass flow rate. It therefore can be used to simulate the performances of hydronic snow melting systems with different design variations. The accuracy of this model depends on not only the modeling algorithms but also the accuracy of weather data and parameters describing the simulated system. Therefore, obtaining accurate information of crucial parameters and weather data, including pavement thermal properties and the snowfall rate, is of great importance to accurately simulate the performance of hydronic snow melting systems. While this model reasonably predicts the surface temperature during most of the storm event, it over-predicts the surface temperature in the final drying period when residual surface water is being evaporated. This may due to the fact that the model neglects the penetration of water into the pavement. Further research of the thermal effects of water penetration is accordingly recommended. This is not a significant disadvantage in using the model in system design since it is the initial heating and snow melting process, rather than final drying of the surface, which are of primary concern. Acknowledgements This material is based on work supported by the Federal Highway Administration (FHWA). Earlier funding, that helped establish the basis of the work, was provided by the Oklahoma Department of Transportation and US Department of Energy and is gratefully acknowledged. References [1] N.M. Schnurr, D.B. Rogers, Heat transfer design data for optimization of snow melting systems, ASHRAE Transactions 76 (1) (197) [2] I.B. Kilkis, Design of embedded snow melting systems: part 2, heat transfer in the pavement a simplified model, ASHRAE Transactions 1 (2) (199) 3 1. [3] J. W Ramsey, M.J. Hewett, T.H. Kuehn, S.D. Petersen, Updated design guidelines for snow melting systems, ASHRAE Transactions 15 (1) (1999) [] M. Leal, P.L. Miller, An analysis of the transient temperature distribution in pavement heating installations, ASHRAE Transactions 7 (2) (1972) [5] N.M. Schnurr, M.W. Falk, Transient analysis of snow melting systems, ASHRAE Transactions 79 (2) (1973) [6] A.D. Chiasson, J.D. Spitler, S.J. Rees, M.D. Smith, A model for simulating the performance of a pavement heating system as a supplemental heat rejecter with closed-loop ground-source heat pump systems, ASME Journal of Solar Energy Engineering 122 (2) [7] S.J. Rees, J.D. Spitler, X. Xiao, Transient analysis of snow-melting system performance, ASHRAE Transactions 1 (2) (22) [] D. Espin, Experimental and computational investigation of snow melting on a hydronically heated concrete slab, M.S. thesis, Oklahoma State University, Stillwater, OK, 23. [9] Liu, X., S.J. Rees, J.D. Spitler. Modeling snow melting on heated pavement surface Part I: model development. Journal of Applied Thermal Engineering, in press, doi:1.116/j.applthermaleng [1] M.D. Smith, Task.6.1 testing of a medium-scale bridge deck heating system. Quarterly Progress Report of the Geothermal Smart Bridge Project, Oklahoma State University, Stillwater, OK, [11] ASHRAE, ASHRAE handbook HVAC applications, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta, 23 (Chapter 5). [12] R.L. Elliot, F.V. Brock, M.L. Stone, S.L. Sharp, Configuration decisions for an automated weather station network, Applied Engineering in Agriculture 1 (1) (199) [13] X. Liu, Modeling and simulation of hydronic snow melting systems, Ph.D. thesis, Oklahoma State University, Stillwater, OK, 25. [1] CECW-EH, Engineering and design: runoff from snowmelt, Department of the Army, US Army Corps of Engineers, Washington, DC, 199. [15] R. Levinson, H. Akbari, Effects of composition and exposure on the solar reflectance of Portland cement concrete, LBNL-33, Heat Island Group, Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, 21.