A New Approach to Modeling Vehicle-Induced Heat and Its Thermal Effects on Road Surface Temperature [Journal of Applied Meteorology and Climatology]
(Journal of Applied Meteorology and Climatology Via Acquire Media NewsEdge) ABSTRACT
The distribution of vehicle-induced wind velocity in the transversal direction of roads is measured. A statistical analysis is also performed to find the vehicle stopping time and stopping position at traffic signals. These results are used to build a heat-balance model to predict the road surface temperature resulting from the thermal effects of vehicles. To validate the model, measured and calculated road surface temperatures for a free-running (single path) location and a traffic-signal location are compared. The contributions of meteorological and vehicle-induced heat fluxes to the road surface temperature are quantitatively analyzed. For the present traffic and meteorological conditions, the calculated and measured road surface temperatures were in agreement for both the free-running and traffic-signal locations. Furthermore, the thermal contribution of vehicles to the road surface temperature was found to be nonnegligible at both locations.
(ProQuest: ... denotes formulae omitted.)
The road surface temperature affects the safety of roads in winter and the thermal environment (such as heat islands) in urbanized areas. The heat-balance method used to predict the road surface temperature requires an accurate evaluation of the heat factors that influence the road surface. However, in contrast to the stochastic method, the heat-balance method does not require the correlations between the road surface temperature and natural factors (meteorology, topography, etc.) or artificial factors (traffic, salting, etc.) at specific points. The heat-balance method is, therefore, more versatile and adaptable than are statistical methods for the prediction of spatial variation in road surface temperatures. In particular, the thermal effects of traffic on road surface temperatures are usually nonnegligible in urban areas, while in mountainous and suburban areas, natural factors are more important. Surgue et al. (1983) reported that recorded road surface temperatures were usually several degrees Celsius higher in the road where traffic was heaviest. Gustavsson and Bogren (1991) showed road surface temperature differences of 1.58C due to the differences in traffic conditions. Fujimoto et al. (2008) showed that the temperature in the vehicle-passage area, over which vehicles pass directly, was approximately 38C lower than that in the non-vehicle-passage area, over which vehicles do not pass directly during a sunny winter day. Furthermore, Fujimoto et al. (2010) reported that the road surface temperature under vehicles waiting at traffic signals was 38-48C higher than that nearby.
These observations indicate that the thermal effects of vehicles on the road surface temperature are not negligible at traffic signals or when the volume of traffic is high.
b. Previous studies on thermal effects of vehicles and their modeling
Heat-balance models have been reported by Sass (1992), Shao and Lister (1996), Rayer (1987), Chapman et al. (2001), and Crevier and Yves (2001), among others. Unfortunately, these models did not include heat gain or loss through the road surface associated with passing vehicles. Recently, several researchers have modeled the thermal effects of vehicles on the road surface temperature. For example, by performing outdoor experiments, Ishikawa et al. (1999) built the first model incorporating longwave radiative heat from the bottom surface of the vehicle (hereafter referred to as the vehicle radiative heat). Prusa et al. (2002) showed the quasi-steady energy balance in the effective range of the vehicle-related heat (DM) surrounding a vehicle and evaluated the thermal fluxes generated by vehicles such as the surface thermal flux owing to frictional loss of a vehicle, radiant flux from a vehicle, sensible heat flux that occurs between theDMand the road surface, and so on. It is of interest that many heat fluxes in the energy balance equation in the DM are expressed using physical and thermodynamic laws. However, it is essential that we discuss whether the road surface temperature over the DM represents the temperature on the road surface in the vehicle-passage area and the relation between the vehicle-induced velocity and the eddy velocity that is the characteristic velocity of the largest eddies in the DM when using their model. Although Sato et al. (2004) indicated that the turbulent momentum transfer is enhanced by the eddy in the wake of a running vehicle, the effect of the turbulent momentum transfer on the road surface temperature was not reported quantitatively by analytical and experimental approaches. Watanabe et al. (2005) modeled the heat transmitted from the vehicle tires due to the friction between the tire and the road surface (hereinafter referred to as the tire frictional heat) and the shielding of solar radiation and sky radiation when the vehicle covers the road surface (hereinafter referred to as the vehicle's shield). Takahashi et al. (2006) proposed a heat-balance model considering the vehicle radiative heat and the vehicle's shield. The observed road surface temperatures for National Route 5 were compared with the calculated ones to find the accuracy of their model, but they did not show the increment or decrement of the road surface temperature due to the traffic conditions.
Subsequently, Fujimoto et al. (2008) developed a heat-transfer model by adding sensible heat due to the air movement by passing vehicles to the model built by Watanabe et al. These heat and air movements are hereafter referred to as the vehicle-induced sensible heat and vehicle-induced wind, respectively. We refer to this model as the vehicle road surface temperature (VRST) model. Fujimoto et al. (2008) also examined the thermal effects of vehicles on the road surface temperature by performing a numerical simulation using both an instantaneous and a time-averaged VRST model. The former calculates the time variation in vehicleinduced heat fluxes associated with the passage of vehicles (under pulselike conditions). The latter calculates the road surface temperature using time-averaged vehicleinduced heat fluxes. The following trends were observed: 1) the thermal effects of vehicles lowered the road surface temperature during the day and raised it at night and 2) the difference in the road surface temperatures of the two VRST models was small. Fujimoto et al. (2010) then conducted a simulation analysis of the road surface temperature at a traffic-signal location where vehicles repeatedly stop and start. The results showed that vehicles starting and stopping at traffic signals caused fluctuations in the road surface temperature, and that the temperature continuously fluctuated around 08C (zero crossing).
Thus, the VRST model has made it possible to extract the properties of the road surface temperature overlooked in previous studies, by conducting experiments to identify heat transfer coefficients and variables relevant to traffic by field and indoor experiments using vehicles with tires. However, the VRST model has the following limitations:
1) Spatial changes in the vehicle-induced wind velocity are not considered (currently, the wind velocity at the center of the vehicle is used as a representative value).
2) At traffic-signal locations, it is assumed that vehicle stopping times and positions are fixed.
3) The VRST model has not been satisfactorily validated. A quantitative comparison of the calculated and observed road surface temperatures has not yet been performed at a traffic signal.
c. Purpose of study
This study had the following major objectives:
1) to derive a rational relationship between the vehicle speed and vehicle-induced wind velocity on the basis of the distribution of vehicle-induced wind velocity in the transversal direction of the road,
2) to elucidate the properties of vehicle stopping time and position at traffic signals,
3) to improve the vehicle-induced sensible heat and vehicle radiative heat using the results obtained from objectives 1 and 2, and
4) to verify the reliability of the improved VRST model by comparing observed and calculated road surface temperatures at a free-running (single path) location and a traffic-signal location.
2. VRST model
The VRST model is based on several assumptions. For vehicle operation, there are three assumptions:
1) The target road surface is the center of the lane (i.e., at the vehicle's centerline). At traffic-signal locations, the center of the vehicle that is stopped just before the stop line is the target road surface.
2) All vehicles travel in the center of the lane and are the same size.
3) The time interval between any two vehicles (the vehicle-passage time) is uniformly distributed on the basis of the hourly traffic volume.
For heat flux, there are two additional assumptions:
4) Heat transfer in the transversal direction of the road is neglected.
5) Additional wind velocity due to the interactions between natural wind and vehicle-induced wind is not considered. That is, there is no superposition of these two winds, and the sensible heat associated with a relatively high wind velocity is incorporated in the heat balance of the pavement surface layer [Eq. (1)].
b. Heat balance on pavement surface
The spikelike changes in heat flux in response to the passing of vehicles are expressed using unit step functions whose values are 0 or 1 [f(t) and g(t)], and the heat balance of the pavement surface layer is given by
where rp is the density of the pavement surface layer (kg m23), cp is the specific heat of the pavement surface (kJ kg21 K21), Tp is the temperature of the pavement surface layer (8C), t is the time (s), Dzs is the thickness of the pavement surface layer (m), Cp is the pavement conductive heat flux (W m22), Rlu is the road surface radiative heat flux (W m22), S is the sensible heat flux (W m22), L is the latent heat flux (W m22), Rld is the sky radiative heat flux (W m22), a is the albedo, Rs is the shortwave (insolation) heat flux (W m22), Ry is the vehicle radiative heat flux (W m22), and Qnet is the net heat flux (W m22). Here, S is given by the following formula based on assumption 5 in section 2a:
where Vnw is the natural (background) wind velocity (m s21), Sa is the natural wind sensible heat flux arising from Vnw (W m22), Vw is the vehicle-induced wind velocity (m s21), and Sy is the vehicle-induced sensible heat flux arising from Vw (W m22). The details of the heat flux in Eqs. (1) and (2) have been described by Fujimoto et al. (2008), and no further explanation is given here. In addition, in this analysis, the road surface is considered to be dry, and, therefore,Lis eliminated. The unit step functions in Eq. (1) will be discussed in detail in the next section.
c. Modeling thermal effects of vehicles
Figures 1a and 1b show the time variations in the heat fluxes due to the passing of vehicles at free-running and traffic-signal locations, respectively.
1) FREE-RUNNING LOCATION
In Fig. 1a, t1 is the period during which the road surface is covered by a moving vehicle (the vehicle-passage time), and t2 is the subsequent period during which it is not covered (the non-vehicle-passage time). The quantities Cp, Rlu, and S act on the road surface at all times. During t1, Ry acts on the road surface while Rld and Rs are zero. Conversely, during t2, Rld and (1 - a)Rs act on the road surface while Ry is zero. The values of t1 and t2 are defined by the following equations:
where Ly is the vehicle length (m), Vy is the vehicle speed (km h21), and Fy is the hourly traffic volume (vehicles per hour).
2) TRAFFIC-SIGNAL LOCATION
In this section, we consider the time taken for a vehicle to stop at the designated point (just before the stop line) after the traffic signal turns red (i.e., the vehicle deceleration time), and the period for which the vehicle remains stationary until the next green signal (vehicle stop time). The stop time at the designated point, t4, is given by
t4 = tredPstPsa, (5)
where tred is the red-signal period that includes the yellowsignal period, Pst (5t40/tred) is the stop-time ratio, and Psa (5Ns/Ns0) is the stopping-vehicle-number ratio. In addition, t40 is the stop time corresponding to the redsignal period (s), Ns0 is the frequency of the red signal per unit time, and Ns is the frequency of the red signal when a vehicle stops at the designated point in Ns0; t40 is the mean of the stop times measured at a traffic signal. As will be discussed in section 4b, Ns and t40 may be affected by the traffic volume.
Finally, from Eq. (5), the vehicle deceleration time, t3 (h), is
t3 = tred - t4. (6)
Given the above thermal effects of vehicles, the unit step functions f(t) and g(t) in Eq. (1) are as listed in Table 1.
3. Measurement and formulation of vehicle-induced wind velocity
a. Outline of experiment
To study the distribution of Vw in the transversal y direction of the road, we conducted an outdoor experiment using a typical passenger vehicle (4.97 m in length, 1.93 m in width, and 1.86 m in height). A thermal anemometer (manufactured by Kanomax) was set up at a height of 0.18 m above the road surface as shown in Fig. 2, and the y direction of Vw was measured by translating the driving of the vehicle in the y direction.
The vehicle's centerline was considered to be y 5 0. The vehicle's speed was set to 30 km h21.
b. Transversal distribution of vehicle-induced wind velocity
Figure 3 shows the time variations in Vw for y* 5 0, 0.4, 1.2, and 1.6, where y* is the normalized distance and y* 5 y/0.5Wy (Wy being the vehicle width). The value of Vw increases rapidly immediately after the vehicle passes (t 5 0), reaching a peak at approximately 1 s and then decreasing gradually.
The maximum value of Vw, Vwmax (m s21), occurred at the center of the vehicle (i.e., y* 5 0) and decreased toward the roadside (as y* became larger). We have normalized Vwmax to express the y direction of Vw in a unified expression:
where Vwmax05Vwmaxj y*50 and Vwmax * 5 0 indicates that Vwmax 5 Vnw.
Figure 4 shows the relationship between Vwmax * and y*. Here, Vwmax * decreases as y* increases, and the relationship between Vwmax * and y* follows a Gaussian function. That is,
V*wmax = exp(-0.31y*2.10). (8)
c. Representative velocity of vehicle-induced wind
In determining the representative value of Vw, Vw, the following assumptions were made:
1) Time variations inVwj y*50 (5Vw0) depend on t but do not depend on y*, as shown in Eq. (9), established by Fujimoto et al. (2008):
where tmax is the time (s) for the wind velocity to reach Vwmax0 from the ambient velocity, t0 is the duration of the vehicle-induced wind, and a, b, and c are coefficients. For vehicle speeds Vy (km h21) ranging from 10 to 70 km h21, these variables and coefficients are formulated in terms of Vy as follows (see Fujimoto et al. 2008):
a = 0.08Vy, (10)
b = 0.28 × 10-2Vy + 0.13, (11)
c = Vwmax0 exp[-b(t0 - tmax)]/(t0 - tmax), (12)
Vwmax0 = 0.08Vy, (13)
tmax = 1.2 exp(-0.3 × 10-2Vy), and (14)
ty = -1.4 × 10-2Vy + 7.6. (15)
In addition, t in Eq. (9) indicates the elapsed time (s) since the vehicle passage.
2) The representative value of Vwmax *, Vwmax *, is the average of Vwmax * over half of the vehicle width (from y* 5 0 to 1.0, the shaded area in Fig. 4).
3) Here, Vw is the product of Vw0 and Vwmax *. On the basis of these assumptions and Eq. (8), Vw is calculated as follows:
4. Micrometeorological observation, traffic-volume survey, and road surface temperature measurement on a national route
a. Outline of observation
This section describes the micrometeorological observations, the traffic-volume survey, and the road surface temperature measurements (hereinafter referred to as the observations). The observations were made at the free-running location and the traffic-signal location, and these are labeled case BS and case CS, respectively. Case BS was measured at National Route 8 (Echizen City, Fukui, Japan) from 0700 to 1700 LT 6 August 2008. Case CS was measured at an intersection on National Route 416 (Fukui City, Fukui) from 1700 to 0800 LT 29-30 December 2009. In both observations, the air temperature Ta and the relative humidity RHa (%) were measured using a thermohygrometer (HMP45, manufactured by Vaisala). The value of Vnw (m s21) was measured using a vane anemometer (Weather Wizard III, manufactured by Davis). Both Rs and Rld were measured using a radiation balance meter (CNR1, manufactured by Kipp and Zonen). These values were recorded every minute by a datalogger. The road surface temperature Ts was measured using a radiation thermometer (ST 60, manufactured by Raytek) at points within and outside the vehicle's passage. Furthermore, the spatial distribution of the road surface temperature was regularly recorded using a thermotracer (TH9100, manufactured by NEC). In case BS, Vy was calculated by measuring the traveling time between two different positions. In case CS, the green-light period tgrn, tred, t4, and the vehicle-stopping positions near the traffic signal were recorded using a video camera.
b. Observation results
Figures 5 and 6 show the time variations in Ta, RHa, Vnw, Rs, Rld, and Fy for cases BS and CS, Vy for case BS only, and tgrn, tred, and t4 for case CS only.
1) FREE-RUNNING LOCATION
The weather on the day of observation was fine until 1200 LT, and then it became cloudy. The road surface was completely dry all day. The value of Ta increased from 23.18C at 0700 LT to 34.88C at 1230 LT, which was the maximum temperature during the observation period. Subsequently, Ta was around 308C until 1700 LT. The value of RHa decreased from approximately 80% at 0700 LT to approximately 40% at 1000 LT. Subsequently, RHa varied within a range of 40%-60%, while Vnw was below 1 m s21 until 1200 LT and reached a maximum of 2.4 m s21 at 1300 LT. Subsequently, Vnw was in the range 0.5-2.0 m s21, and Rs increased from the beginning of the observation to a maximum of 908 W m22 at 1200 LT. It then oscillated because of the effect of the clouds. The value of Rld ranged from 420 to 475 W m22, while Fy ranged from 270 to 500 vehicles per hour with an average value of 376 vehicles per hour. In addition, Vy varied between 37 and 42 km h21 with an average value of 38 km h21.
2) TRAFFIC-SIGNAL LOCATION
During the observation period, the weather was fine and the road surface was dry. The value of Ta decreased from 5.78C at the beginning of the observation to 1.08C at 0000 LT and then increased to around 2.08C, while RHa was 60%-70% throughout the observation period. For most of the time, Vnw was less than 0.4 m s21, and the maximum Vnw of 0.7 m s21 was reached at 0100 LT. The value of Rld was approximately 300 W m22, while Fy decreased from approximately 360 vehicles per hour from 1700 to 1900 LT to a minimum of 51 vehicles per hour at 0400 LT. Throughout the observation period, tgrn was approximately 30 s, while tred was approximately 90 s from 1700 to 2000 LT and ranged from 60 to 75 s for the rest of the observation period. Furthermore, t4 was almost equal to tred at 1700 and 1800 LT but became shorter as Fy decreased, reaching a minimum of 16 s at 0400 LT.
Figures 7 and 8 show the relationship between Pst or Psa and Fy. The value of Pst increased in proportion to the power function of Fy and is given by
Pst = 0.02F0.64 (18)
The relationship between Psa and Fy is given by the same type of function as that for the relationship between Pst and Fy:
Psa = 0.30F0.18y. (19)
5. Comparison of measured and calculated results of road surface temperature
a. Boundary conditions and initial conditions
A numerical analysis of the road surface temperature was performed for a pavement body of thickness 0.5 m and a subgrade of thickness 4.9 m. To obtain the initial temperatures in the pavement and subgrade, we entered weather data for August and December (from Fukui Local Meteorological Observatory) into the model and carried out a transient analysis until the vertical temperature profile varied with the thermal equilibrium state. The weather and traffic data obtained from the observations were used as the boundary conditions and were given by a linear interpolation of the data collected in time order. The temperature of the bottom boundary of the analysis area was fixed at 158C in case BS and 108C in case CS. In addition, on the basis of assumption 4 in section 2, it was considered that there was no heat transfer at the side boundary of the analysis area. Since Vy could not be measured in case CS, it was fixed to 32 km h21 with reference to the Fiscal 2005 Road Traffic Census. Table 2 lists the thermophysical property values given in a heat-transfer handbook (written by the Japan Society of Mechanical Engineers in 1993, pp. 238 and 375) for the pavement and ground used in the analysis.
b. Spatial distribution and time variation of road surface temperature
The model was validated by comparing the observed Ts with the calculated Ts.We also discuss the difference in Ts between the vehicle-passage and non-vehiclepassage areas.
1) FREE-RUNNING LOCATION
Figures 9a and 9b show the spatial distribution of Ts in case BS at 0635 and 1157 LT 6 August 2008. In Fig. 9a we see that Ts at all points (A-F) was almost uniform, in the range 27.28-27.88C, whether or not vehicles were passing. However, the values of Ts at points G, J, I, and L in the vehicle-passage area in Fig. 9b (50.68-53.68C) were approximately 18-38C lower than Ts at points H and K without vehicle passage (54.48-54.88C).
Figure 10 shows the time variation in Ts in case BS. Hereinafter, the suffixes y and n for Ts indicate the vehicle- and non-vehicle-passage areas, respectively, and the suffixes m and c indicate the measured and calculated values, respectively.
The initial Tsvm and Tsnm were both 30.68C, and there was no difference between them: DTsm (5Tsvm - Tsnm) 5 0. Both Tsvm and Tsnm increased over time, but Tsnm became higher than Tsvm at around 0900 LT. Both values reached a maximum at 1200 LT (Tsnm 5 55.58C and Tsvm 5 51.28C) with DTsm524.38C. Subsequently, both temperatures decreased gradually while maintaining DTsm ' 21.58C. The average DTsm during the observation period DTsm was 22.08C.
The calculated temperatures, Tsvc and Tsnc, reproduced the observed values in general, as shown in Fig. 10. However, when the vehicle-induced sensible heat Sy is deleted from the heat balance in Eq. (1) [i.e., S 5 Sa in Eq. (1)], the calculated road surface temperature T9svc was slightly lower than Tsnc and became more inaccurate than Tsvc. As far as the present traffic and meteorological conditions are concerned, it is seen that Sy cannot be disregarded from the calculation of the road surface temperature.
During the observation period, the average difference between Tsvc and Tsnc, DTsc (5Tsvc - Tsnc), was 22.08C, which was in good agreement with DTsm.
2) TRAFFIC-SIGNAL LOCATION
Figures 11a and 11b indicate the spatial distribution of Ts in case CS at 2102 and 2103 LT 29 December 2009. It is evident from Fig. 11a that the vehicle-body temperature is higher than Ts except on the roof, side-view mirrors, and so on. The values of Ts at points M, N, and O in the non-vehicle-passage area were 7.28, 8.68, and 9.58C, respectively. Here, Ts increased as the measurement point was closer to the vehicle-passage area. In Fig. 11a, the values of Ts at points P, S, R, and U in the vehicle-stopping area were 38-48C higher than Ts at pointsQand T in the zone where vehicles did not stop or did not pass.
According to Prusa et al. (2002), the width of the DMis 1.7-3.9 times that of a vehicle. Consequently, it is clear from Fig. 11 that the road surface temperature over the DM is not uniform. There is an obvious difference in the road surface temperature between the vehicle-passage area and the non-vehicle-passage area. The road surface temperature in the vehicle-passage area can be regarded as the representative surface temperature on the road that is subject to the vehiclerelated heat.
Figure 12 shows the time variations in Ts in case CS. At the beginning of the observation Tsvm and Tsnm were 10.98 and 8.28C, respectively. Slight fluctuations in the temperature continued throughout the observation period. At the beginning of the observation, DTsm was 2.78C, reaching 4.98C at 2000 LT and then decreasing over time. After 0100 LT, DTsm was approximately 0.58C and the value of DTsm was 1.98C.
While Tsnc varied gradually over time, Tsvc showed fluctuations with a small amplitude. The top-right graph in Fig. 12 shows an enlarged view of the time variation in Tsvc (solid line). It is evident that Tsvc decreased for tgrn (shown as A) and increased for tred (shown as B and C). The cause of the fluctuation will be discussed in detail in section 6a(2).
The amplitude for Tsvc, DTsvc, was approximately 0.38C for Fy 5 360 vehicles per hour at 1700-1900 LT, approximately 0.28C for Fy 5 225 vehicles per hour at 0000 LT, and lower than 0.18C for Fy 5 51 vehicles per hour at 0400 LT. Increases in Fy tended to increase DTsvc.
The values of Tsnc and Tsvc were in good agreement with the measured temperatures, Tsnm and Tsvm. In addition, DTsc was 1.68C, which was 0.38C lower than DTsm. This difference between DTsc and DTsm may depend on the temperature measurement position on the road surface and may be caused by an error in the initial temperature of the pavement body or subgrade.
a. Heat balance on road surface
1) FREE-RUNNING LOCATION
Figures 13a and 13b show the time variation in heat flux in the non-vehicle-passage area from 0700 to 1700 LT 6 August 2008 and in the vehicle-passage area for 20 s from 1105:30 to 1105:50 LT 8 August 2008 in case BS. The positive vertical (y) axis (top half) and the negative y axis (bottom half) indicate the heat gain and loss, respectively, of the road surface layer.
We first discuss the heat flux in the non-vehicle-passage area in Fig. 13a. The main causes of heat gain were (1 2 a)Rs and Rld, while Rlu and Cp before 1300 LT and Rlu and S 5 Sa after 1300 LT were the main causes of heat loss. The values of Rlu and Cp were almost constant at approximately 2573 and 2339 W m22.
We now consider the heat flux in the vehicle-passage area in Fig. 13b. For the t1 period (0.4 s), (1 2 a)Rs and Rld were zero because of the vehicle's shielding effect, but were 645 and 451 W m22, respectively, for the t2 period (9.1 s). Instead, an Ry of 547 W m22 acted on the road surface for the t1 period. The maximum value of Sa was 2136 W m22 when Vnw . Vw, and the maximum value of Sy reached 2409 W m22 (53 times larger than Sa) when Vnw , Vw. It is seen that Sy contributes to the decrease in the road surface temperature shown in Fig. 10 (i.e., Tsvc , T9svc), and that a running vehicle plays the role of a fan that cools the road surface.
2) TRAFFIC-SIGNAL LOCATION
Figures 14a and 14b show the time variations in the heat flux in the non-vehicle-passage area from 1700 to 0800 LT 29 December 2009 and in the vehicle-passage area for 3 min from 0000 LT 30 December 2009 in case CS.
In the non-vehicle-passage area in Fig. 14a, the heat loss by Rlu and heat gain by Rld were dominant, and S 5 Sa, Cp, and (1 - a)Rs were relatively small.
We now discuss the heat flux in the vehicle-passage area in Fig. 14b. The values for t1, t2, t3, and t4 during this period were 0.5, 4.1, 34.3, and 35.9 s, respectively. For the t2 and t3 periods, Rld was 319 W m22 and reached zero for the t1 and t4 periods. For the t1 and t4 periods Ry, was 369 W m22. The maximum value of Sa was 216 W m22 when Vnw . Vw, and Sy reached a maximum value of 2164 W m22 when Vnw , Vw. Here, Cp increased as if to compensate for the negative Sy for tgrn and reached a maximum value of 54 W m22, but decreased for tred. The value of Rlu was 2332 W m22.
The average Qnet values for the t1, t2, t3, and t4 periods were 11, 272, 16, and 39 W m22, respectively.
The minute fluctuations in Tsvc described in section 5b (2) are caused by abrupt changes in Qnet (from positive to negative and vice versa) associated with the thermal effects of the vehicle.
b. Evaluation of thermal effects of vehicles
Figure 15 shows a schematic view of the heat balance in the vehicle-passage area (left) and that in the nonvehicle-passage area (right). The contribution of heat flux (Rld, Rlu, Rs, Cp, Ry, and S) to DTsc was quantitatively evaluated as IP* by the following equation:
where P2y is the heat flux in the vehicle-passage area (Rld-y, Rlu-y, Rs-y, Cp-y, Ry-y, and S-y) and P-n is the heat flux in the non-vehicle-passage area (Rld-n, Rlu-n, Rs-n, Cp-n, and S2n). Note that P* is the hourly heat flux calculated by the time integration of the subtraction of P-n from P-y. Thus, IP* is the rate of each P* with regard to the sum of the absolute values of P*. A positive IP* increases DTsc and a negative IP* reduces DTsc.
Next, let us consider IP* at the free-running and traffic-signal locations based on Figs. 16a and 16b, which show the time variations in IP* for cases BS and CS, respectively.
1) FREE-RUNNING LOCATION
At the free-running location, IRy * and IRlu * were always positive, but IRld * and IRs * were always negative because of the vehicle's shielding effect. In addition, IS* was positive at 1300, 1400, and 1600 LT. This was because Tsvc , Tsnc and Vnw was large. Conversely, ICp* IRy * was positive until 1200 LT and negative at 1300, 1400, and 1600 LT. This was due to the increase in Cp-n associated with a drop in Tsnc.
The values of IRld * , IRlu * , IRs *, ICp*, IRy *, and IS*, which are the means of IP* over the analysis period, were 20.15, 0.10, 20.14, 0.17, 0.18, and 20.16, respectively. At the free-running location, it was difficult to identify the dominant heat flux that affects DTsc.
2) TRAFFIC-SIGNAL LOCATION
At the traffic-signal location, IRy * and IRld * played an important role in IP* and the contributions of IRlu * , IS*, and ICp* to Tsc were relatively small. However, the absolute values of IRlu * , IS*, and ICp* increased slightly toward 0400 LT, when Fy reached its minimum. Because of this increase, IRy * and IRld * decreased, but they were approximately 3 times larger than the absolute values of IRlu * or IS*. At 0400 LT, the values of IRlu * , IS*, and ICp* were 20.07, 0.12, and 20.10, respectively.
The values of IRld * , IRlu * , IRs *, ICp*, IRy *, and IS* were 20.38, 20.04, 0.00, 0.04, 20.08, and 0.46, respectively. At the traffic-signal location, Ry and Rld are the main heat fluxes that affect DTsc. However, the effects of Rlu, S, and Cp on DTsc are nonnegligible when Fy becomes small.
We measured the distribution of the vehicle-induced wind velocity in the transversal direction of roads, and used a video camera to statistically evaluate the characteristics of vehicle stopping time and position at trafficsignal locations. Using these results, we developed a heat-balance road surface temperature model that considers the thermal effects of vehicles. The measured road surface temperatures were compared with the temperatures calculated by the proposed model at a free-running (single path) location and a traffic-signal location. This clarified the thermal effects of vehicles on the road surface temperature.
Our results are as follow:
1) The maximum value of the vehicle-induced wind velocity appeared at the center of the vehicle and decreased toward the roadside, following a Gaussian distribution.
2) The ratio of the vehicle-stopping period to the redlight period increased with an increase in traffic volume, following a power function. For example, this ratio was 0.25 for a traffic frequency of 50 vehicles per hour and 0.87 for 360 vehicles per hour.
3) The ratio of the number of vehicles stopping at the designated point (just before the stop line) to the total number of stopping vehicles decreased from 0.90 to 0.50 following a power function, as the traffic volume decreased.
4) For both the free-running and traffic-signal locations, the calculated road surface temperatures in the vehiclepassage area and the non-vehicle-passage area were in agreement with the observed values.
5) The computation revealed the following two points: (i) the vehicle passage at the traffic-signal location causes fluctuations in road surface temperature with a small amplitude-the road surface temperature drops during the green-light period and increases during the red-light period, and (ii) the amplitude of the fluctuations in the road surface temperature tends to increase slightly as the traffic volume increases.
6) At the free-running location, it was difficult to identify the dominant heat flux that influenced the difference in the road surface temperature between the vehicle-passage area and the non-vehicle-passage area. At the traffic-signal location, the vehicle relative heat flux and sky relative heat flux were the main contributors to this difference.
Although traffic and weather conditions were limited, the proposed model enabled the calculation of the time variation in the road surface temperature in the vehiclepassage area and direct comparison with the observed one. Consequently, it was found that the thermal contribution of vehicles to road surface temperature cannot be neglected and is significantly different between the free-running location and the traffic-signal location. However, further studies will be needed to find the limitations of the parameterizations and formulation of the vehicle-related heat fluxes in this study through the change in vehicle size and vehicle speed.
Acknowledgments. This work was supported by KAKENHI (90456434).
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AKIHIRO FUJIMOTO, AKIRA SAIDA, AND TERUYUKI FUKUHARA
Graduate School of Engineering, University of Fukui, Fukui, Japan
(Manuscript received 1 August 2011, in final form 17 May 2012)
Corresponding author address: Akihiro Fujimoto, Graduate School of Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui City, Fukui 910-8507, Japan.
List of Symbols
a, b, c Coefficients regarding Vw0
Cp Pavement conductive heat flux (W m-2)
cp Specific heat of the pavement surface (kJ kg-1 K-1)
Fy Hourly traffic volume (vehicles per hour)
f(t), g(t) Unit step functions (0 or 1) to express the spikelike changes in heat flux in response to the passing of vehicles
IP* Rate of each P* with regard to the sum of the absolute values of P*
IP* Mean values of IP* over the analysis period
L Latent heat flux (W m-2)
Ly Vehicle length (m)
m, c Suffixes expressed as the measured and calculated values
Ns Frequency of the red signal when a vehicle stops at the designated point in Ns0
Ns0 Frequency of the red signal per unit time
Psa Stopping-vehicle-number ratio (5Ns/Ns0)
Pst Stop-time ratio (=t40/tred)
P-n Heat flux in the non-vehicle-passage area (Rld-n, Rlu-n, Rs-n, Cp-n, and S-n)
P-y Heat flux in the vehicle-passage area (Rld-y, Rlu-y, Rs-y, Cp-y, Ry-y, and S-y)
P* Hourly heat flux calculated by the time integration of the subtraction of P-n from P-y
Qnet Net heat flux (W m-2)
Rld Sky radiative heat flux (W m-2)
Rlu Road surface radiative heat flux (W m-2)
Rs Shortwave (insolation) heat flux (W m-2)
Ry Vehicle radiative heat flux (W m-2)
RHa Relative humidity (%)
S Sensible heat flux (W m-2)
Sa Natural wind sensible heat flux arising from Vnw (W m-2)
Sy Vehicle-induced sensible heat flux arising from Vw (W m-2)
Ta Air temperature (8C)
Tp Temperature of the pavement surface layer (8C)
Ts Road surface temperature (8C)
Tsvc 9 Calculated road surface temperature without vehicle-induced sensible heat (8C)
t Time (s)
t0 Duration of the vehicle-induced wind (s)
t1 Period during which the road surface is covered by a moving vehicle (the vehicle-passage time) (s)
t1 Period during which the road surface is covered by a moving vehicle (the vehicle-passage time) (s)
t3 Vehicle deceleration time (s)
t4 Stop time at the designated point (s)
t40 Stop time corresponding to the red-signal period (s)
tgrn Green-light period (s)
tmax Time for the wind velocity to reach Vwmax from the ambient velocity (s)
tred Red-signal period (s)
Vnw Natural (background) wind velocity (m s-1)
Vy Vehicle speed (km h-1)
Vw Vehicle-induced wind velocity (m s-1)
Vw Representative value of Vw (m s-1)
Vwmax Maximum value of Vw, (m s-1)
Vwmax0 Vwmax at y* 5 0 (m s-1)
Vwmax * Normalized Vwmax
Vwmax * Average of Vwmax * over half of the vehicle width
Vw0 Vw at y* = 0 (m s-1)
y, n Suffixes expressed as the vehicle- and nonvehicle-passage areas
Wv Vehicle width (m)
y Transversal direction of the road (m)
y* Normalized distance
rp Density of the pavement surface layer (kg m-3)
Tsv - Tsn
Amplitude for Tsvc
Dzs Thickness of the pavement surface layer (m)
DTs The average DTs during the observation period
(c) 2012 American Meteorological Society
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