Arantza Ugalde
email: augalde@obsebre.es

Eduard Carcolé
email: eduard@zisin.geophys.tohoku.ac.jp

Carlos A Vargas
email: cavargasj@unal.edu.co

S-wave attenuation characteristics in the Galeras volcanic complex (south western Colombia)

Keywords: Coda waves; scattering, intrinsic absorption, Galeras volcano

A c c e p t e d M a n u s c r i p t Abstract Vertical-component, short period seismograms from 435 well located volcano-tectonic earthquakes are used to estimate S-wave attenuation in the Galeras volcanic complex (south western Colombia) using coda waves. The coda magnitudes (M c ) of the events are less than 2. Event depths are less than 10 km and hypocentral distances up to 16 km.

Intrinsic absorption (Q i -1 ) and scattering attenuation (Q s -1 ) are estimated by means of a fitting procedure between the observed and synthetic coda envelopes in four frequency bands (1)(2)(2)(3)(4)(4)(5)(6)(7)(8)(8)(9)(10)(11)(12). The observations are compared with the theoretical predictions by an accurate approximate analytical solution of the radiative transfer equation which is based on the assumptions of multiple isotropic scattering, impulsive isotropic point source, and a medium with homogeneous scattering and absorption properties. Results show that scattering is strong and it constitutes the predominant attenuation effect in this region. In the frequency range analyzed in this study the values of the mean free path for scattering of S waves range between 2.7 8.1 l  km, which are clearly higher than those obtained in other volcanic regions of the world, but about two orders of magnitude smaller than average estimates for the Earth's crust. The scattering due to the interaction of seismic waves with the heterogeneities of the medium (when they are on a length scale close to the seismic wavelength) and intrinsic absorption due to anelasticity. The inverse quality factors,

1 i Q  and 1 s Q  characterize
intrinsic absorption, and scattering attenuation, respectively, so total attenuation is the sum of the two types:

-1 -1 -1 t i s =+ Q Q Q .
Many studies have been conducted to determine which process, intrinsic absorption or scattering, dominates total attenuation (see [START_REF] Sato | Seismic wave propagation and scattering in the heterogeneous earth[END_REF]. Multiple scattering models for S-coda envelope synthesis have been used to separate the contribution of intrinsic absorption and scattering to total attenuation of S waves. [START_REF] Hoshiba | Simulation of multiple scattered coda wave excitation based on the energy conservation law[END_REF] estimated higher-order solutions of the multiple isotropic scattering model using numerical techniques. However, it is possible to obtain and use analytical solutions [START_REF] Zeng | Scattered wave energy propagation in a random isotropic scattering medium, I, Theory[END_REF][START_REF] Sato | Energy transportation in one-and two-dimensional scattering media: analytic solutions of the multiple isotropic scattering model[END_REF]. [START_REF] Hoshiba | Numerical basis of the separation of scattering and intrinsic absorption from full seismogram envelope: a Monte-Carlo simulation of multiple isotropic scattering[END_REF] and Fehler et al. (1992) developed the Multiple Lapse Time Window Analysis (MLTWA) to separately estimate the intrinsic absorption and scattering loss, within the framework of a model of multiple isotropic scattering in a medium with uniform distribution of scattering and absorption properties, S-wave-only scattering, constant S-wave velocity and spherically symmetrical radiation from an impulsive point source. In their method, the integrated energy density over three consecutive time windows from the S-wave arrival time is evaluated as a function of the source-receiver distance [START_REF] Hoshiba | Separation of scattering attenuation and intrinsic absorption in Japan using the Multiple Lapse Time Window Analysis of full seismogram envelope[END_REF]. Therefore, the observed energy density is compared with the energy predicted by theoretical models to obtain the estimated scattering (g) and absorption (h) coefficients. The total attenuation, The computation of the energy density from theoretical models based on multiple isotropic scattering involves the evaluation of time-consuming two-dimensional integrals [START_REF] Zeng | Scattered wave energy propagation in a random isotropic scattering medium, I, Theory[END_REF] or Monte Carlo simulations [START_REF] Hoshiba | Simulation of multiple scattered coda wave excitation based on the energy conservation law[END_REF], which are still more time-consuming. There are two approximate solutions of the radiative transfer equation in the literature for the computation of the scattered seismic wave energy density for multiple isotropic scattering [START_REF] Zeng | Compact solutions for multiple scattered wave energy in time domain[END_REF][START_REF] Paasschens | Solution of the time-dependent Boltzmann equation[END_REF]. The Paasschens' (1997) expression, which is shown to be accurate and numerically very [START_REF] Sens-Schönfelder | Radiative transfer theory for estimation of the seismic moment[END_REF].

In this study, we will focus on the estimation of S-wave attenuation in the Galeras volcanic complex (south western Colombia). Galeras was designated a Decade Volcano in 1991, which identified it as a target for intensive and interdisciplinary study during the United Nations' International Decade for Natural Disaster Reduction.

Interdisciplinary research (geological, geophysical and geochemical) has been conducted in the region since the re-activation of Galeras volcano. However, to the best of our knowledge, no systematic investigation of S-wave attenuation characteristics has been performed in this region. [START_REF] Moncayo | Temporal variation of coda-Q at Galeras volcano, Colombia[END_REF] analyzed the temporal variation of the phenomenological parameter coda-Q (Q c ) using a single-scattering model in the Galeras volcano region. Carcolé et al. (2006) imaged the small-scale heterogeneities in the same region by estimating the three-dimensional spatial distribution of relative scattering coefficients by means of a S-coda envelope inversion method. The purpose of the present study is to estimate the scattering and absorption coefficients in the Galeras volcano region. This additional contribution to the knowledge of the internal structure and properties of the Galeras volcano is of considerable practical interest because the attenuation parameters of seismic waves in the lithosphere are valuable for seismic hazard assessment in the region. For this purpose, we will use an alternative method to analyze the contribution of intrinsic absorption and scattering to total attenuation by means of a coda envelope-fitting method using the Paasschens' (1997) solution. This method is particularly useful when the characteristics of the seismic data available do not allow using the MLTWA, as discussed in section 4. joint inversion of S-coda envelopes for source and site parameters, as well as for medium parameters assuming the theoretical model of [START_REF] Paasschens | Solution of the time-dependent Boltzmann equation[END_REF]. [START_REF] Matsunami | Seismic attenuation in a nonvolcanic swarm region beneath Wakayama, southwest Japan[END_REF] and Del Pezzo et al. (2006) used a method based on a fitting process of the theoretical S-coda model by [START_REF] Zeng | Compact solutions for multiple scattered wave energy in time domain[END_REF] to an average S-coda envelope.

Some other methods have been used to analyze volcanic areas (e.g., [START_REF] Wegler | Scattering behaviour at Merapi volcano (Java) reveled from an active seismic experiment[END_REF][START_REF] Wegler | Analysis of multiple scattering at Vesuvius volcano, Italy, using data of the TomoVes active seismic experiment[END_REF][START_REF] Wegler | Diffusion of seismic waves in a thick layer: theory and application to Vesuvius volcano[END_REF]. Their results will be compared and discussed in section 5.

A c c e p t e d M a n u s c r i p t 5

Geotectonic setting and data

The Galeras volcanic complex, which is located in the Central Cordillera of the south western Colombian Andes (Figure 1), has been intermittently active for >1 Ma. The eastern summit, called Galeras volcano (1.23°N, 77.36°W; summit elevation 4,276 m), is a 4,500 years old andesitic stratovolcano that is historically the most active volcano in Colombia. The tectonics of the region result from a complex interaction between the Nazca plate to the west and the South America plate to the east, which causes the uplift of the Andes and the volcanism in the region. The main tectonic feature is the Romeral fault zone, which at the same time, constitutes one of the main structural elements in Colombia. It includes the Silvia-Pijao and Buesaco faults that cross under the volcano structure with a N40°E trend (Figure 1). The evolution history of the complex includes two caldera-forming eruptions (560 ka and 40 ka ago, respectively), a summit collapse, which occurred between 12 ka and 5 ka, and the present-day small cone-building style of eruption (Calvache et al., 1997).

Galeras volcano has been re-activated frequently in historic times and, although it has a short-term history (<5000 years) of relatively small-to-moderate scale eruptions, the volcanic complex has been able to produce major and hazardous eruptions. Lava flows account for more than 95% of the volcano's activity for more than 1 Ma, but modest in size explosive eruptions have also occurred during the past 10 ka and have produced pyroclastic flows frequently (Banks et al., 1997). Galeras rises 1600 m above the city of San Juan de Pasto, the capital of the State of Nariño, which is located only 9 km east from the active crater. Thus, the volcano poses potential risk to a population of more than 300,000 in Pasto and to another 100,000 people living in the flanks of the complex.

A c c e p t e d M a n u s c r i p t 6 One of the four longest repose periods accounted by historical records lasted from 1948 to 1988. Then, the re-activation of Galeras volcano was recognized [START_REF] Williams | Premonitory geochemical evidence of magmatic reactivation of Galeras volcano, Colombia[END_REF] and the eruptive period continued until 1995. This period included at least 6 explosive eruptions recorded mainly between 1992 and 1993. Since then, the volcano stayed in a relative calm stage with some ash and gas emission episodes and low-level eruptive activity (a crater located to the east of the main one was re-activated in 2002 after more than 10 years of inactivity Seismicity in the region since 1988 has been characterized by long-period events, volcano-tectonic earthquakes and tremor episodes. A type of unusual shallow-source, low-frequency seismic signals called "tornillos" (screws), which are related to magmatic activity, have also been recorded during different stages of volcanic activity at Galeras [START_REF] Gómez | Unusual low-frequency volcanic seismic events with slowly decaying coda waves observed at Galeras and other volcanoes[END_REF]. The level of seismic activity has fluctuated between periods of low-level activity and episodes of increased earthquake rate and/or magnitude. Some shallow (up to 8 km) volcano-tectonic earthquakes have reached local magnitudes up to 4.7.

Data used in this study consist of records from 435 volcano-tectonic earthquakes over the period from 1989 through 2002 (Figure 1). 1)

was used for the locations, which were carried out by [START_REF] Moncayo | Temporal variation of coda-Q at Galeras volcano, Colombia[END_REF]. The shortperiod (T 0 =1 s), vertical component recording stations used (31 locations in total) did not operate continuously through time because of various modifications in the network configuration. The combination of telemetric and portable stations used were located at distances less than 10 km from the active crater. The recorded ground motions were digitized at a rate of 100 samples per second; the whole system has a flat velocity response between 1 and 25 Hz.

A c c e p t e d M a n u s c r i p t 8

Theoretical background

Multiple isotropic scattering processes may be modelled by using the radiative transfer theory for the energy density [START_REF] Ishimaru | Wave propagation and scattering in random media[END_REF]. The radiative transfer (or Boltzmann) equation (RTE) can be solved exactly in the Fourier space for one, two, three and four dimensions. [START_REF] Zeng | Scattered wave energy propagation in a random isotropic scattering medium, I, Theory[END_REF] obtained an exact compact integral solution for the real three-dimensional space. In order to simplify the computations, it is possible to develop approximations of the exact solution of the RTE in three dimensions. [START_REF] Paasschens | Solution of the time-dependent Boltzmann equation[END_REF] proposed The solution has the form:

                a 2 3 18 2 2 2 2 4 a 3/ 2 22 33 42 3/ 2 3 1 4 1 ( , ) ( ) exp exp 4 1 exp exp 1 ( ) 43
( ) 8(3 ) ! N N P r t r vt vt l vt l r r v t vt r vt l vt l G vt r l v t l vt N x G x x NN                              (1)
where v is the wave velocity, l is the mean free path for scattering, l a is the absorption length which are related to the scattering, g, and absorption, h, coefficients by g=1/l and h=1/l a . Θ(x) is the step function, which is zero for x<0 and 1 for x>0. It is possible to approximate G(x) within a few percent of error as

( ) exp( ) 1 2.026 / G x x x 
. In equation ( 1), P(r,t) represents the intensity of wave radiation spreading from the source through the medium, at distance r and time t. Prior to this analysis, a data selection process was performed in order to discard those seismograms with saturated S-wave arrivals or poor signal-to-noise ratios. Then, each seismogram was bandpass-filtered over the frequency bands 1-2 (1.50.5) Hz, 2-4 (31)

Hz, 4-8 (62) Hz, and 8-12 (102) Hz, using eight-pole Butterworth filters. The upper frequency limit is determined by the signal energy contents of the available data, which decays abruptly for frequencies f above 12 Hz. The rms amplitudes   obs ,, A f r t were calculated from the bandpass-filtered data by using a time window length for the averaging of t2 s for the frequency band centered at 1.5 Hz; t1 s for the 3 and 6 Hz centre frequencies; and t0.5 for the 10 Hz centre frequency. All the time windows were spaced 0.5 s. Only data with a signal-to-noise ratio greater than 2 were considered. For this study, aimed to retrieve S-wave attenuation features, only vertical component data were available. Although it has been shown that the coda analysis is independent of the component of the particle ground motion (e.g., [START_REF] Hoshiba | Separation of scattering attenuation and intrinsic absorption in Japan using the Multiple Lapse Time Window Analysis of full seismogram envelope[END_REF], the lack of horizontal component recordings to measure the direct S-wave energy may affect the final results.

Noise

The envelope fitting method is particularly useful for the present application, because the short distance range (from 1 to 16 km) and the short duration of the S-wave coda preclude the use of the MLTWA. Depending on the frequency of interest, from 72% to 95% of the data with acceptable signal-to-noise ratios have lapse time windows of less than 25 s in length. However, in principle, the observed envelopes can be fitted to the synthetic ones which are calculated using equation (1) for any hypocentral distance or lapse time window. Therefore, to find the best fit model parameters g and h we performed a grid search between the observed (   2 obs ,, A f r t ) and synthetic (   2 syn ,, A f r t ) envelopes against lapse time for all the available seismograms. Before the nonlinear fitting process was performed, we smoothed the synthetic envelopes by using the same time window lengths for the averaging as for the observed data. This step is very important because the smoothing process alters the shape of the envelopes. Note that if the smoothing is not performed in the synthetic envelope, it is impossible to fit it to experimental data due to the presence of a delta function in equation (1).

We devised a convenient best-fitting scheme on a logarithmic scale for the ith seismogram that involves the minimization of the misfit function:

        2 2 2 2 obs syn 1 1 ln , , ln , , N i i j i j i j A f r t A f r t c N         (2)
N i i j i j j c A f r t A f r t N           
accounts for the site and source effects and it is considered constant for a single frequency. N is the number of points of the time window considered. We stress in this point that in this method it is not necessary to choose an arbitrary reference time in order to carry out a normalization of the waveforms. Notice that the normalization process, which is needed in the other methods such as the MLTWA, may be sensitive to coda fluctuations and may introduce some errors in the computation of both g and h.

To automate the process, and inspired in the procedure used by [START_REF] Wegler | Scattering behaviour at Merapi volcano (Java) reveled from an active seismic experiment[END_REF], we considered the start time (t 1 ) of the window used for the nonlinear fit as marked by the S-wave travel time,  in order to use the envelope-fitting method. In this study, the S-wave velocity distribution was computed for each waveform using / S v r t  (see also [START_REF] Wegler | Scattering behaviour at Merapi volcano (Java) reveled from an active seismic experiment[END_REF] which gives a mean value of v=2.23 km/s with a standard deviation =0.27. The assumption of a half space is certainly a limitation of the proposed methodology, since estimates of g and h may depend on the velocity structure of the region, as pointed out by [START_REF] Hoshiba | Scattering attenuation and intrinsic absorption using uniform and depth dependent model -Application to full seismogram envelope recorded in Northern Chile[END_REF].

Final values for g and h for the study region are obtained by averaging the single estimates from every envelope for each analyzed frequency band.

A c c e p t e d M a n u s c r i p t 14

Results and Discussion

Attenuation parameters

Figure 3 shows an example of the best-fitting theoretical envelopes along with the observed ones against time for each frequency band studied. In this example the g and h estimates are within one standard deviation of the mean g and h values for all the analyzed frequency bands. All the estimated values and averages are plotted in Figure 4, where each small circle represents g and h from a single seismogram. We note that, after the visual inspection of the whole seismograms collection, that corresponded to 435 earthquakes recorded at 31 stations during 14 years (September, 1988to June, 2002), we got 1953 seismograms, and after the strict quality control procedures considered in the computing processes, we only got final results for 110 seismograms at 1.5 Hz, 399 seismograms at 3 Hz, 183 seismograms at 6 Hz, and 50 seismograms at 10 Hz centre frequencies. The mean attenuation parameters ( g , h , and their inverses l and a l ) for the study region were obtained by averaging the g, h, l and l a estimates computed for every single hypocenter-station path. They are shown in Table 2, together with the corresponding 1 i Q  (intrinsic absorption), 1 s Q  (scattering attenuation) and 1 t Q  (total attenuation) mean values, which were calculated from g and h by considering an average S-wave velocity value of 2.23 v  km/s. Fitting 2 shows that, on average, g values are a factor of 3 to 10 greater than h estimates, which indicate that scattering is predominant over intrinsic absorption for the studied frequencies.

1 i Q  , 1 s Q  and 1 t Q  in Table 2 to the frequency law 11 0 ( ) ( )• Q f Q f f      we obtained that 1 0i Q   (11.62.1)•10 -3 , i   0.70.1; 1 0 s Q   (21.84.7)•10 -2 , s   1.40.1; and 1 0t Q   (22.34.5)•10 -2 , t   1.30.1.
A comparative plot of the average attenuation parameters and1 t Q  as a function of frequency (Table 2) is shown in Figure 5. It is observed that scattering strongly prevails over intrinsic absorption for all frequencies, indicating that total attenuation is mainly determined by the scattering loss in the Galeras volcanic complex region.

1 i Q  , 1 s Q  ,
Finally, Figure 6 shows the dependence of g and h estimations on the hypocentral distance in the Galeras volcano region. The envelope fitting method does not require to consider homogeneity for the maximum travel distance range, as in the MLTWA. Thus, a distance dependence of the attenuation parameters can be observed. In Figure 6 g appears to decrease as hypocentral distance increases for all the frequency bands analyzed. According to the events and stations distribution in the target region (see Figure 1), larger hypocentral distances correspond to larger depths of the hypocenter.

Thus, this result may suggest a decrease of heterogeneity with depth in the Galeras volcano region. As for the intrinsic absorption coefficient, no clear trend is observed in Figure 6.

Comparison with other volcanic regions

The predominance of scattering over intrinsic dissipation has been found in other volcanoes. [START_REF] Wegler | Scattering behaviour at Merapi volcano (Java) reveled from an active seismic experiment[END_REF] studied the seismic structure of the Merapi volcano (Java) using recordings of artificial shots. They adopted the diffusion model for coda envelope analysis and found that the scattering attenuation is at least one order of A c c e p t e d M a n u s c r i p t 17 which were also consistent with those obtained for Mount Etna (Del Pezzo et al., 1996).

The characteristic length scale of intrinsic absorption in the Galeras volcanic complex region gives values of 25 77 a l  km. These values are of the same order of magnitude as the usual average findings for other regions (e.g., [START_REF] Sato | Energy transportation in one-and two-dimensional scattering media: analytic solutions of the multiple isotropic scattering model[END_REF]Fehler, 1998, Figure 7.12, Lemzikov, 2008), however, the typical length scale for the intrinsic attenuation in this work is at least one order of magnitude larger than the estimates by [START_REF] Wegler | Analysis of multiple scattering at Vesuvius volcano, Italy, using data of the TomoVes active seismic experiment[END_REF] and [START_REF] Wegler | Scattering behaviour at Merapi volcano (Java) reveled from an active seismic experiment[END_REF] at the Vesuvius and Merapi volcanoes, respectively.

In view of the different methods used in the different studies, it is worth examining the assumptions inherent in ours. Therefore, one has to be extremely careful when getting conclusions.

Influence of the assumptions of the physical model considered

The assumptions underlying the physical model used in this study are similar to those that many researchers used in other regions of the world. The theoretical model used assumes spherically symmetric radiation from the source, although radiated energy is always nonspherical [START_REF] Sato | Seismic wave propagation and scattering in the heterogeneous earth[END_REF]. The nonspherical radiation from the earthquake source causes a variation in amplitude near the direct S-arrival. Figure 4 shows scatter among the individual g and h estimates for each frequency band that may be due to fluctuations in the absorption and scattering properties of the crust, but also possibly biased by the anisotropy of the source radiation pattern.

However, the anisotropy of scattering and the vertical heterogeneity of the medium are the most important factors that can bias our estimates from reality. Scattering patterns are nonisotropic in general, and forward scattering strength increases with where cos is the average cosine of the scattering angle. This implies an important but unknown error in the computation of the mean free paths.

Another factor the model does not take into account is the radiative loss into a weakly scattering mantle [START_REF] Margerin | Radiative transfer and diffusion of waves in a layered medium: New insight into coda Q[END_REF][START_REF] Margerin | Residence time of diffuse waves in the crust as a physical interpretation of coda Q: Application to seismograms recorded in Mexico[END_REF]. Using the diffusion approximation, [START_REF] Wegler | Diffusion of seismic waves in a thick layer: theory and application to Vesuvius volcano[END_REF] derived interesting analytical expressions for the coda decay including the leakage of energy from a heterogeneous layer over a homogeneous half-space. He applied the model to seismic data from an active seismic experiment at Vesuvius volcano and he found that there was a trade-off between the intrinsic attenuation and the thickness of the scattering layer. Therefore, a bias to the estimate of h can be introduced by assuming a simple statistically homogeneous half-space model.

Nevertheless, analytical solutions of the radiative transfer equation for a medium with such effects incorporated simultaneously (nonspherical radiation pattern of the source, anisotropy of scattering and inhomogeneity of the scattering and absorption properties)

have not yet been found. The approximate method that we use is convenient and could be improved, but is not discrepant with results from previously-used methodologies.

A c c e p t e d M a n u s c r i p t 19

Conclusions

Using a coda-envelope-fitting-method, the scattering and intrinsic absorption strengths (g and h) have been estimated for the Galeras volcanic complex region of south western

Colombia. The synthetics are calculated by means of the approximate solution of the radiative transfer equation in 3-D given by [START_REF] Paasschens | Solution of the time-dependent Boltzmann equation[END_REF]. The method gives a single estimate of the attenuation parameters for each hypocenter-station path and it does not require choosing an arbitrary reference time in order to normalize the waveforms. The method appears to be particularly useful when the dataset characteristics, as in the case of the Galeras volcanic complex, do not allow applying the MLTWA. However, it seems that the envelope fitting method could be used to analyze any other region.

Results show that the scattering mechanism predominates in the attenuation process in with the prediction for best-fitting g and h parameters using equation (7) (solid line) for an earthquake with hypocentral distance r=7.4 km. and Seismological Pasto Observatory, pers. comm.).

Table 2. Average S-wave attenuation parameters for the analyzed frequency bands in the Galeras volcanic complex region. A c c e p t e d M a n u s c r i p t

  attenuation in the Earth is caused by two major mechanisms:

   , where  and v are the angular frequency and S-wave velocity, respectively. The MLTWA has been successfully applied to separate the contribution of scattering and intrinsic absorption from total attenuation under the hypothesis of multiple isotropic scattering in many regions of the Earth (seeUgalde et al. (2007, Figure 10) for a comparison of Q t -1 , Q i -1 , and Q s -1 versusfrequency for different regions in the world). Recently, high resolution maps of Japan for the seismic S-wave attenuation parameters have been obtained by using the MLTWA with data provided by the Hi-net seismic network(Carcolé and Sato, 2009).Results show strong regional variation of the parameters that depend mainly on the tectonic setting of each region and volcanism mechanisms. Although the MLTWA is based on very simple hypotheses (multiple isotropic scattering in a medium with homogeneous distribution of scattering mean free path and intrinsic absorption) the results are very informative on the characteristics of each region, and show the usefulness of studying the properties of scattered seismic waves in the understanding of the properties of the crust.

  been applied to seismological data byAbubakirov (2005) and Sens-

  to the MLTWA have been proposed to estimate intrinsic and scattering attenuation. In particular, Sens-Schönfelder and Wegler (2006) used a

  an algebraic expression which uses the interpolation between exact solutions of the RTE for the 2-D and 4-D cases. It was successfully used by Abubakirov (2005) in a MLTWA for the Kamchatka lithosphere. Sens-Schönfelder and Wegler (2006) also used the Paasschens' (1997) formulation to obtain source spectra and seismic moments.

  advantages in using an algebraic expression for synthesizing the multiple scattered wave envelopes. A very important one is the computation time, which is considerably less than for the two-dimensional integration process involved in the numerical calculation of the exact solution of the RTE. On the other hand, equation (1) is a very convenient expression that allows developing alternative methods to the MLTWA that can be used in any region of the world. envelope fitting method and data analysisThe simplicity of the computation of the multiple scattered wave envelopes by means of equation (1) allows using alternative methodologies to the MLTWA for estimating empirically the intrinsic absorption and scattering contributions to total attenuation. In this paper we propose fitting every observed envelope by the synthetic model of[START_REF] Paasschens | Solution of the time-dependent Boltzmann equation[END_REF] (equation (1)). For this purpose, we will compute the observed meansquared (MS) seismogram envelopes ( ) against lapse time for all the available narrow bandpass-filtered waveforms with center frequency f and then, a nonlinear fitting procedure will be performed between the observed and the smoothed synthetic envelopes ( ), which are calculated using equation (1) as a function of h (=1/l a ) and g(=1/l).

  was estimated from 5 s of data preceding the P onset. Typical examples of a function   obs ,, A f r t for three actual seismograms used are shown in Figure 2. All the

  this work show clear impulsive onsets for P and S waves and a short coda.

St

  , reading on each seismogram, as information on the direct S-wave energy is required to separate intrinsic and scattering attenuation The end of the time window (t N ) corresponds to S t +12 s. This value was chosen by reaching an agreement between having the longest time window length for the fit above the noise level and rejecting the minimum data files as possible. Information on the direct S-wave energy is required to separate intrinsic and scattering attenuation. In fact, the MLTWA analyzes data starting from S t . On the other hand, we compared the results obtained for several time window lengths (from 10 to 15 s from S t ) and they were inside the error bounds, which assures the stability of the method. The coda envelope decay after 2 S t (which corresponds to a lapse time of 14 s for the most distant event) shows a linear behavior for all the events. A total of 3•10 6 pairs (g, h), g=n*0.001 (n=1,2,3,…,3000); h=m*0.001 (m=1,2,3,…,1000) for the synthetic energy were searched for the best fit. It is mandatory A c c e p t e d M a n u s c r i p t 13 to calculate a theoretical velocity for each seismogram using the equation / S v r t

  Sato and Fehler (1998, p. 214) showed that strong forward scattering increases the amplitude just after the direct-wave arrival, and weak backward scattering decreases the amplitude of the late S-coda as compared to the isotropic scattering case.Abubakirov (2005) noted that the scattering coefficient g obtained within the framework of the multiple isotropic scattering model corresponds roughly to g e /2, where g e is the effective scattering coefficient. This effective scattering coefficient is related to the true anisotropic scattering coefficient g s by the equation cos

Figure 1 .

 1 FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. Examples of the velocity recording (top) and rms amplitudes (bottom) for

Figure 3 .

 3 Figure 3. (Left) Example of the bandpass-filtered mean squared amplitudes (small dots)

Figure 4 .

 4 Figure 4. Estimates of g (top) and h (bottom) as a function of frequency. A dot indicates

Figure 5 .Q

 5 Figure 5. Comparative plot of 1 i Q  , 1 s Q  , and 1 t Q  as a function of frequency.

Figure 6 .

 6 Figure 6. Plots of g (left) and h (right) as function of hypocentral distance for the four

  n is the sample size. The error intervals represent the 95% confidence intervals (1.96 / n  ).

  Figure 1 Click here to download high resolution image

  Figure 2 Click here to download high resolution image

  Figure 3 Click here to download high resolution image

  Figure 4 Click here to download high resolution image

  Figure 5 Click here to download high resolution image

  Figure 6 Click here to download high resolution image

TABLE CAPTIONS Table 1 .

 CAPTIONS1 Layered velocity structure model considered (Diego Gómez, Vulcanological

TABLE 1

 1

	Table 1
	Depth (km) S-wave velocity (km/s)
	4	2.0
	2	2.1
	0	2.2
	-4	3.4
	-22	3.8
	-40	4.5

TABLE 2

 2

	Center frequency,
	Hz	g , km -1	h , km -1	l , km	a l , km	1 x10 3 i Q 	1 Q  x10 2 s	1 Q  x10 2 t
	1.5	0.453±0.043	0.033±0.006	2.7±1.4	77.1±19.0	7.9±1.4	10.7±1.0	11.5±1.2
	3.0	0.448±0.024	0.048±0.002	2.8±0.2	36.1±4.9	5.6±0.4	5.3±0.2	5.9±0.2
	6.0	0.329±0.039	0.063±0.004	4.4±0.4	20.9±2.4	3.7±0.2	1.9±0.2	2.3±0.2
	10.0	0.191±0.043	0.053±0.008	8.1±1.4	24.8±5.1	1.9±0.2	0.7± 0.2	0. 9±0.2

Table 2

 2

Acknowledgments

We are very grateful to the people of the Observatorio Vulcanológico y Sismológico de Pasto, Colombia, for providing us with the seismic data used in this study. We thank the Editor, George Helffrich, and two anonymous reviewers for suggestions that significantly improved the manuscript. This work started when one of the authors (E. C.) was under a "Juan de la Cierva" contract of the Spanish Ministerio de Ciencia y Tecnologia (MCYT). E.C. is now enjoying a fellowship of Global Center of Excellence program for Earth Science in Tohoku University, Sendai, Japan. This research has been partially supported by the MCYT projects CGL-2005-04541-C03-02/BTE and CGL2008-00869/BTE.

A c c e p t e d M a n u s c r i p t 16 magnitude larger than intrinsic absorption. They obtained an extremely short mean free path of the order of 0.1 l km for the frequency range 4-20 Hz. [START_REF] Wegler | Analysis of multiple scattering at Vesuvius volcano, Italy, using data of the TomoVes active seismic experiment[END_REF][START_REF] Wegler | Diffusion of seismic waves in a thick layer: theory and application to Vesuvius volcano[END_REF] obtained similar results for Mt. Vesuvius. He again modeled coda envelopes from an active seismic experiment using the diffusion model and found a mean free path for S waves of 0.2 l km for center frequencies between 2 and 16 Hz.

Del Pezzo et al. (2006) obtained different results for Mt. Vesuvius (see also [START_REF] Ugalde | Comments on "Separation of Q i and Q s from passive data at Mt. Vesuvius: A reappraisal of the seismic attenuation estimates[END_REF]Del Pezzo et al., 2009). These authors, using volcano-tectonic earthquakes, estimated values of the mean free path for scattering of 0.7 l km for frequencies centered at 3 and 6 Hz and 5 l  km for frequencies greater than 6 Hz for one station, and 0.5 l km for the whole frequency range at a second station. They concluded that the diffusion regime was appropriate to model the coda envelopes at Vesuvius volcano.

Very recently [START_REF] Yamamoto | Multiple scattering and mode conversion revealed by an active seismic experiment at Asama volcano, Japan[END_REF] studied the shallow part of Asama volcano on the basis of the radiative tansfer theory using the multiple isotropic scattering model including mode conversions. Using data from an active seismic experiment they obtained a mean free path for scattering of about 1 km for the frequency band 8-16 Hz.

In the present work, we have obtained values of 2.7 8.1 l  km for frequencies ranging from 1 to 12 Hz. These values are higher than the ones obtained in the Vesuvius, Merapi and Asama vicinities, but they are still much lower than the usual regional measurements reported throughout the world (e.g., Sato and Fehler, 1998, Figure 3.10). Our estimates for the mean free path for scattering are also lower than those obtained by [START_REF] Lemzikov | Estimation of shear-wave attenuation characteristics for the Klyuchevskoi volcanic edifice[END_REF] Ugalde A. and Carcolé, E., Phys. Earth Planet. Int., 173: 195-196, doi: 10.1016/j.pepi.2008.10.002. Fehler, M., M. Hoshiba, H. Sato, and Obara, K., 1992. Separation of scattering and intrinsic attenuation for the Kanto-Tokai region, Japan, using measurements of Swave energy vs. hypocentral distance, Geophys. J. Int., 108: 787-800.


Lena Stawreberg
email: lena.stawreberg@kau.se

Lars Nilsson

Modelling of Specific Moisture Extraction Rate and Leakage Ratio in a Condensing Tumble Dryer

Keywords:

The use of tumble dryers in households is becoming more common. Tumble dryers, however, consume large amounts of electric energy. A statistical model over the tumble dryer is created from a design of experiments. The model will be used to find the best settings for the power supply to the heater, the internal airflow and the external airflow in order to reach a high specific moisture extraction rate (SMER) and a low leakage ratio of water vapour. The aim also involves explaining the trends of the SMER and the leakage ratio based on the physics of the tumble dryer drying process. A statistically significant model, which can be used for improving the SMER and leakage ratio, was established from 19 experiments in a condensing tumble dryer. The results show that a high power supply to the heater, a high internal airflow and a low external airflow give the highest SMER values. This combination of settings also results in the largest leakage ratio values for the dryer. Leakage is most affected by the external airflow.

Introduction

Tumble dryers are common devices in ordinary households. They offer a fast and convenient way of drying textiles, independent of weather conditions. Their disadvantage, however, is their large consumption of energy, i.e. electricity. The energy use of one unit is small considering the large number of existing dryers and how often they are used, the total energy use is considerable. Since 1990, the clothes drying energy consumption in the OECD countries has risen by 32.7% to 77.1TWh in 2000, International Energy Agency [START_REF]InternationalEnergyAgency, Cool Appliances -Policy Strategies for Energy Efficient Homes[END_REF]. It is therefore highly desirable to reduce the energy use of these products.

There are mainly two types of dryers available on the market today; the venting tumble dryer and the condensing tumble dryer. The condensing tumble dryer is becoming more frequently used in households. This type of dryer has the advantage that all heat supplied to the dryer eventually ends up in the laundry room. This is especially beneficial in the Scandinavian climate. Additionally, it does not require ducting to exhaust the moist air to the outside making it easy to install. There is, however, a leakage of water vapour from the internal system of the dryer, which should be minimised in order to avoid high humidity in the laundry room. The third type of dryer available is equipped with a heat pump. According to Braun et al. [START_REF] Braun | Energy Efficiency Analysis of Air Cycle Heat Pump Dryers[END_REF] and Bansal et al. [START_REF] Bansal | Improving the Energy Efficiency of Conventional Tumbler Clothes Drying Systems[END_REF], the air cycle heat pump dryer was found to be significantly more efficient than the traditional tumble dryer. The cost of this dryer, however, is considerably higher than the cost of a traditional tumble dryer.

A few studies are found in the literature in which the condensing tumble dryer has been investigated regarding its energy use. According to Bansal et al. [START_REF] Bansal | Improving the Energy Efficiency of Conventional Tumbler Clothes Drying Systems[END_REF], the energy efficiency of a condensing tumble dryer is 7% higher than that of the venting tumble dryer. This was determined from a computer model of the dryer. Conde [START_REF] Conde | Energy Conservation with Tumbler Drying in Laundries[END_REF] and Hekmat and Fisk [START_REF] Hekmat | Improving the Energy Performance of Residential Clothes Dryers[END_REF], however, state that the condensing tumble dryer has an increased energy use compared with the venting tumble dryer. Conde [START_REF] Conde | Energy Conservation with Tumbler Drying in Laundries[END_REF] used a computer model in combination with experiments, whereas the investigation made by Hekmat and Fisk [START_REF] Hekmat | Improving the Energy Performance of Residential Clothes Dryers[END_REF] was based on measurements. Cochran et al. [START_REF] Cochran | Condensing Dryers with Enhanced Dehumidification Using Surface Tension Elements[END_REF] found a significant improvement in the energy efficiency of the condensing tumble dryer by incorporating surface tension elements instead of the traditional air to air heat exchanger. According to Liu et al. [START_REF] Liu | Modeling and Performance Investigation of a Closed-Type Thermoelectric Clotehs Dryer[END_REF], the optimal performance of a condensing tumble dryer using thermoelectric elements instead of the air to air heat exchanger strongly depends on the intensities of the drying air temperature, the electric power and the total weight of the clothes.

In order to improve the performance of the condensing tumble dryer, a model of the process can be useful. Theoretical models have been made by Deans [START_REF] Deans | The Modelling of a Domestic Tumbler Dryer[END_REF], Lambert et al. [START_REF] Lambert | Modelling as a Tool for Evaluating the Effects of Energy-Saving Measures. Case Study. A Tumbler Drier[END_REF], Yadav and Moon [START_REF] Yadav | Modelling and Experimentation for the Fabric-Drying Process in Domestic Dryers[END_REF], and Ah Bing and Shiming [START_REF] Bing | A New Termination Control Method for a Clothes Drying Process in a Clothes Dryer[END_REF] regarding the venting tumble dryer. Due to the recycling of air, a more complex theoretical model is required to describe the drying process of the condensing tumble dryer as compared to the venting tumble dryer. The components of the condensing tumble dryer are densely placed, which makes it difficult to perform accurate measurements in the dryer, measurements that could be used for validating a theoretical model. This speaks for the use of a design of experiments, i.e., a method that provides a way to create a statistical model of the process using a low number of experiments.

The design of experiments has been found to be a useful tool for studying drying processes, and especially for making improvements to existing dryers. This method was used for optimising a combined drying process (infrared and infrared-convective drying) of a porous medium in a study carried out by Dutournie et al. [START_REF] Dutournie | Optimization of Radiant-Convective Drying of a Porous Medium by Design of Experiment Methodology[END_REF]. They performed experiments with four factors and three responses, and they chose a full factorial central composite design. Dutournie et al. [START_REF] Dutournie | Optimization of Radiant-Convective Drying of a Porous Medium by Design of Experiment Methodology[END_REF] concluded that the use of experimental designs could be a powerful method for obtaining optimal operating conditions for a dryer, especially in combined drying. The response surface method has been applied by Theppaya and Prasertsan [START_REF] Theppaya | Optimization of Rubber Wood Drying by Response Surface Method and Multiple Contour Plots[END_REF] to optimise the drying of rubber wood, by Madamba and Lopez [START_REF] Madamba | Optimization of the Osmotic Dehydration of Mango (Mangifera Indica L.) Slices[END_REF] to optimise the osmotic dehydration of mango slices and by Hammami and Rene [START_REF] Hammami | Determination of Freeze-Drying Process Variables for Strawberries[END_REF] to determine the freeze-drying process variables for strawberries. Nitz and Taranto [START_REF] Nitz | Drying of Beans in a Pulsed Fluid Bed Dryer: Drying Kinetics, Fluid-Dynamic Study and Comparisons with Conventional Fluidization[END_REF] investigated the drying of beans in a pulsed bed dryer using an experimental design whose results were used for creating a model of the process. An experimental design was also performed by Lopes da Cunha et al. [START_REF] Lopes Da Cunha | Effects of Operating Conditions on the Quality of Mango Pulp Dried in a Spout Fluidized Bed[END_REF], who studied the drying of mango powder in a spout fluidised bed dryer.

The aim of this study is to use a design of experiments in order to create a statistical model over the condensing tumble dryer. The model will be used to find the best settings for the power supply to the heater, the internal airflow and the external airflow in order to reach a high specific moisture extraction rate (SMER) and a low leakage ratio. The aim also involves explaining the trends of the SMER and the leakage ratio based on the physics of the tumble dryer drying process.

Material

The condensing tumble dryer consists of the main components as shown in Fig. 1, i.e., a rotating drum containing the wet textiles, two fans, a heat exchanger and an electric heater. The drying process in a condensing tumble dryer can be described in terms of three stages considering the drying air: humidification, dehumidification and heating.

Humidification of the air takes place inside the drum when the internal airflow encounters the wet textiles. The temperature of the air decreases as the humidity of the air increases. The air is dehumidified in the heat exchanger which is cooled with room air. The humidity of the air is reduced and the temperature is lowered. Finally, the drying air is heated in the electric heater at constant humidity leading to a reduction in relative humidity. The drum has an inner diameter of 570 mm and a length of 390 mm.

The size of the cross flow plate heat exchanger is 230 mm wide, 90 mm high with a length of 320 mm and consists of 10 horizontal plates.

Four different periods are recognised during the drying cycle of a condensing tumble dryer: (1) the heating period, (2) the constant drying rate period, (3) the falling drying rate period, and (4) the cooling period. In the heating period, the wet textiles are heated until an equilibrium temperature is reached and the constant drying rate period begins. The drying rate remains constant until the water at the surface of the textiles has evaporated. During the falling drying rate period, when water is transported from within the textiles to the surface, the temperature of the drying gas leaving the drum increases.

When the textiles have reached the desired moisture content according to the chosen drying program, the cooling period begins during which time no power is supplied to the heater of the dryer.

Method

Statistical model for SMER and leakage ratio

A design of experiments was used to identify significant factors and to determine how they interact. The power supply to the heater, the internal and the external airflows were studied as factors affecting the performance of the dryer. The experiments were laid out in a symmetrical fashion around five standard reference experiments. Each factor was varied between a maximum and minimum value as shown in Table 1. The software used for the study was MODDE 7.0.

The responses were: [START_REF]InternationalEnergyAgency, Cool Appliances -Policy Strategies for Energy Efficient Homes[END_REF] the specific moisture extraction rate -SMER

[g/kJ] determined by tot Wo Wi Q m m SMER - = , (1)
and ( 2) the leakage of water expressed in percentage of the total evaporated mass of water according to

L V = m Wi -m Wo -m C m Wi -m Wo . ( 2
)
The SMER shows the ratio between the amount of evaporated water and the total energy supply. A high SMER would indicate an efficient drying process with low energy losses. The leakage of water from the tumble dryer is an important parameter, both for reducing energy losses from the process and for preventing a humid environment in the laundry room.

For this study, a quadratic regression model was chosen with a central composite facecentred (CCF) design. This is a standard design supporting a quadratic model describing linear relations, quadratic relations and interactions between the factors according to (Eriksson et al. [START_REF] Eriksson | Design of Experiments Principles and Applications[END_REF]):

. The power supply to the heater and that to the motor rotating the drum and the fans of the dryer was registered for each test run. Mean values over ten seconds were measured with an accuracy of ± 1%. The power supply to the heater was adjusted by on-off regulation with a set target value. The mean value of the measured power supply during each test was used in the analysis. All power supplied to the heater was assumed to increase the temperature of the internal airstream. The power supply to the motor rotating both fans and the drum was 145W.

ε β β β β β β β β β β + + + + + + + + + + = E I E h I h E I h E I h V V V Q V Q V V Q V V Q y heater, T hx , see
Three different impellers were used to regulate the internal airflow according to the values in the experimental design set at 88m 3 /h, 77m 3 /h and 66m 3 /h, respectively. The internal airflow over the electric heater was determined from tests performed with a dry load according to

) ( hx h p I h I T T c Q V - = ρ & & . ( 4
)
The external airflow was reduced by covering the inlet duct and it was determined from the assumption that the energy loss from the internal airflow passing through the heat exchanger was transferred completely to the external airflow. As the tests were performed with a dry load, the external airflow was determined by ) (

) ( HXi HXo E hx f I I E T T T T V V - - = ρ ρ & & . ( 5
)
The external airflow in the original dryer was 155 m 3 /h. By covering the inlet duct the external airflow was reduced to 113 m 3 /h and 72 m 3 /h.

Physical model for SMER

The following assumptions were made in the physical model over the drying process in the condensing tumble dryer:

• relations are determined only for the constant drying rate period;

• the enthalpy of the drying air is constant over the drum, h h =h f ;

• the relative humidity of the air leaving the drum is 100%;

• the relative humidity remains at 100% throughout the heat exchanger;

• the internal mass flow of dry air is constant throughout the internal system; and

• the heat exchanger is considered infinitely large.

In a condensing tumble dryer all parameters depend on each other, which made it necessary to find a starting point for the calculations. An internal airflow temperature between the heat exchanger and the heater, T hx , was therefore set to a value representing a test run in the dryer. This value for T hx was later verified by a calculated value produced from material and energy balances for all components in the system. The fundamental equations used in the model can be found in Pakowski and Mujumdar [START_REF] Pakowski | Basic Process Calculations and Simulations in Drying[END_REF].

The humidity of the air between the heat exchanger and the heater, Y hx , was calculated from a correlation for air saturated with water vapour, and the enthalpy, h hx , was determined by

) ( 0 h T c Y T c h hx p hx hx p hx V A + + = . ( 6
)
The mass flow of dry air in the internal system was determined by

1 + = hx I I I Y V m A ρ & & , (7)
where the density of the humid air was determined from tabled values of pressure and temperature at a relative humidity of 100% and the ideal gas relation.

The humidity of the air remains constant over the heater, and the temperature of the air after the heater, T h , was determined from

hx hx p p I h h T Y c c m Q T V A A + + = ) ( & & . ( 8
)
The enthalpy, h h = h f , was determined from the temperature and the humidity of the air between the heater and the drum similarly to equation [START_REF] Cochran | Condensing Dryers with Enhanced Dehumidification Using Surface Tension Elements[END_REF]. The humidity of the air leaving the drum, Y f , was calculated from a correlation for air saturated with water vapour.

The heat transfer of the heat exchanger was determined both from the internal and the external airflow. The heat transfer gained by the external airflow over the heat exchanger was

) ( HXi HXo p E E HX T T c V Q - = ρ & & . ( 9
)
The room air temperature was set to 20 °C and the heat exchanger was assumed to be infinitely large. Thus, the temperatures of the external and the internal airflow leaving the heat exchanger had the same value. The heat transfer from the internal airflow was

]} ) ( [ { hx p hx f hx f I hx T c Y Y h h m Q W A - + - = & & . ( 10
)
The condensed water leaving the heat exchanger was assumed to have the same temperature as the internal airflow leaving the heat exchanger. In the ideal process, the internal and external heat transfer should be equal as there would be no heat losses or leakages. However, to be able to relate the results from the model to the investigated tumble dryer, the ratio of the external heat transfer to the internal heat transfer was set to 0.78 in the model due to heat losses and leakages. This value was chosen to give the temperatures in the model a value not exceeding +-10 °C off the measured values of T hx .

In the ideal drying process the SMER for the constant drying rate period is determined by

h hx f I Q Y Y m SMER A & & - = . ( 11
)

Leakage ratio

The leakage ratio depends on the humidity of the internal airflow, the pressure difference between the internal system and the surroundings as well as on the size of the cavities. The area of the cavities will not vary between the different tests implying that there should be a correlation between the humidity, the static pressure and the leakage ratio. By using the measured temperature between the drum and the heat exchanger in combination with the assumption of 100% relative humidity at the drum outlet in the dryer, the humidity of the airflow was determined from a Mollier chart. The influence of the pressure differences on the leakage was not further investigated in this study. As a first approximation, then, leakage ratio depends on the humidity of the circulating air.

Results

The results from the tests performed in the condensing tumble dryer are shown in Table 2. The mean value of the measured power supply to the heater deviates slightly from the target values in the experimental design and has therefore been adjusted to the measured value.

The measured values of the leakage ratio deviated from the normal distribution and were therefore logarithmically transformed. A normal distribution of the response is required in the regression analysis. The statistical model shows good significance.

When interpreting the results from the model, it is important to point out that the deviation between the target values of the power supply to the heater and the actual measured values will make the model unsymmetrical. This can be studied through the condition number, which was 3.7 for this study. For this type of design, it should be in the range of 3-8 according to Eriksson et al. [START_REF] Eriksson | Design of Experiments Principles and Applications[END_REF]. This would mean that the model is acceptable. Another important issue is the interval chosen for the experiments, which is below the settings used for the original dryer. Results from the five standard reference experiments show a good precision as the mean value of SMER was 0.252 ± 0.002g/kJ and the leakage ratio was 37 ± 1.3%.

Interactions including the external airflow (

I E V V & & * and h E Q V & & * )
I h I h E I h V Q V Q V V Q SMER ⋅ + ⋅ - ⋅ + - + - = (12)
No interactions were significant in the correlation for the leakage ratio and only the quadratic coefficient of the power supply to the heater was significant. The logarithmically transformed leakage ratio is, according to equation ( 3), described by

2 6 h E I h V Q V V Q L ⋅ + - + - = . ( 13
)
An ANOVA test shows that the regression models are significant and statistically good for both SMER and leakage ratio. Both the goodness of fit (R2) and the goodness of prediction (Q2) are high. For SMER, R2 is 0.985 and Q2 is 0.963. For leakage, R2 is 0.967 and Q2 is 0.937. A confidence level of 95% was used. There was no lack of fit for any of the models. The model error is in the same range as the pure error and the model shows good fit to the data.

In Fig. 2, the SMER of different power supplies and different external and internal airflows is shown in a surface response plot. Low external airflow and high power supply to the heater gives the highest SMER value. It can also be seen that an increased internal airflow also increases the SMER, especially at high power supply to the heater.

Low internal airflows in combination with high external airflows give the lowest values

for the leakage ratio. The power supply to the heater has a minor effect on the response, as shown in Fig. 3.

The SMER as determined from the physical model over the tumble dryer is shown in Fig. 4 plotted against the values from the statistical model.

The relation between the physical model and the statistical model generated from MODDE can be described by

SMER Physical = 1.17SMER Statistical + 0.06 ( 14
)
with R 2 = 0.87.

Based on the assumption that the humidity of the internal airflow will affect the leakage of water from the dryer, the leakage ratio and the humidity of the internal airflow exiting the drum are plotted against the external airflow in Fig. 5. The leakage ratio presented in the figure is determined from the statistical model, and the humidity is determined from measurements of temperature in the dryer. The relative humidity of the air exiting the dryer was assumed to be 100%. An increased external airflow leads to a decrease in the humidity of the air and thereby also to a decreased leakage ratio.

Discussion

The results from the statistical model show that it is not possible to find settings that simultaneously give a low leakage ratio and a high value of SMER for the investigated tumble dryer. Both the external airflow and the power supply to the heater affect the SMER strongly. In Fig. 2 it can also be seen that there is a significant interaction between the power supply to the heater and the internal airflow; the higher the power supply, the more a change in internal airflow affects the SMER. This could be explained by the increased temperature in the tumble dryer due to a high power supply to the heater, which will lead to increased moisture contents in the internal airflow. An increased internal airflow will therefore be required in order to transport the evaporated moisture from the textiles.

According to the results from the statistical model, the leakage ratio has a strong correlation with the external airflow. A high external airflow gives a low leakage ratio.

In Fig. 3 it can be seen that both a low and a high power supply to the heater give approximately the same leakage. This can be a result of the required drying time. A low external airflow together with a low power supply to the heater will result in a longer drying time. If the process is long, larger leakages can be found if the humidity of the internal airflow is high. It can, however, also be a result of the effectiveness of the heat exchanger related to an increased power supply to the heater. If the cooling of the heat exchanger becomes too low as the humidity of the internal airflow increases, less water will condense in the heat exchanger. The efficiency of the heat exchanger is an important factor, which has also been pointed out by Cochran et al. [START_REF] Cochran | Condensing Dryers with Enhanced Dehumidification Using Surface Tension Elements[END_REF] and Liu et al. [START_REF] Liu | Modeling and Performance Investigation of a Closed-Type Thermoelectric Clotehs Dryer[END_REF]. Changes in the internal airflow will increase or reduce the leakage ratio similarly, independent of external airflow or power supply to the heater. This indicates that changes in the internal airflow will change the static pressure in the internal system. An increased pressure resulting from a higher airflow will lead to an increased leakage ratio. Pressure differences in the system should be further investigated.

The physical model presented in this study is a simplified version using ideal assumptions, for the behaviour of the components and is limited to modelling the conditions during the constant drying rate period. According to Fig. 4 it can be determined that, throughout the study, the values for SMER from the physical model are higher than the ones from the statistical model. It seems to be possible to use a simple ideal model in order to see a trend, but not for achieving accurate values. The physical model shows how the humidity, together with the temperature, will affect the SMER, assuming drying takes place in the period of constant drying rate. It can be seen that there is a correlation between the two models -the higher the temperature and humidity, the higher the SMER. Therefore, it can be concluded that the constant drying rate period has a large influence on the drying process in the condensing tumble dryer.

As the physical model is created from an ideal process, the result from this study shows that the performance of the components in the dryer mainly follows the ideal process in the investigated interval. The physical model, however, will not give any information about which factor is the most important. It should also be pointed out that both the presented models are valid for a specific interval and for a specific tumble dryer.

In Fig. 5 it is shown that an increased external airflow will lead to decreased humidity as well as to a reduced leakage ratio. This agrees with results from both models: the statistical model shows that the leakage ratio decreases with an increasing external airflow, whereas the physical model shows that increasing external airflow (better cooling) leads to a decreased humidity of the circulating air. Unfortunately this poses a problem when trying to combine a high SMER and a low leakage. A higher SMER is achieved as the humidity of the circulating airflow is increased. This, however, directly leads to higher leakage, which is undesirable in the laundry room.

The results from this study imply that the use of a statistical model is a good choice when studying an existing dryer. The presented model can be used for improving the performance of the tumble dryer by finding profitable settings, but also for improved knowledge about the process. When investigating a different type of tumble dryer, a new design of experiments should be made to detect differences between the dryers regarding sealings, the efficiency of the various components, etc.

It is difficult to point out the best settings for the dryer as regards the highest possible SMER and a low leakage ratio, as they do not correlate. Today, the focus of the manufacturers primarily lies on increasing the SMER. It is important to reduce the energy use considering the energy classifications on the market. There is still no official classification system regarding leakage, but the figures are nevertheless often shown in market tests. Leakage is thus an important parameter to reduce considering the environment in the laundry room.

Conclusions

A design of experiments performed in MODDE gives a statistically significant model that can be used as a tool for improving the SMER and reducing the leakage from the condensing tumble dryer.

A high power supply to the heater, a high internal airflow and a low external airflow give the highest SMER value. Both power supply to the heater and the external airflow have a large effect on the SMER according to the model presented by MODDE. A simplified ideal model confirmed that calculations made over the constant drying rate period are representative for the drying process in identifying trends of how SMER changes, but they are not sufficient to provide accurate values.

The leakage ratio is most affected by the external airflow. There is a correlation between the moisture content of the air in the internal system and the leakage ratio at different external airflows. A high moisture content leads to increased leakage.

Nomenclature

Fig. 1 .

 1 The temperatures of the inlet and the outlet external airflow, T HXi and T HXo (also indicated in Fig.1.), and the temperature of the condensed water leaving the dryer, T C , were measured.

  and the quadratic coefficient of the external airflow ( 2 E V & ) were statistically insignificant in the description of SMER. The correlation between the investigated factors and SMER is therefore, according to equation (3

Fig. 1 .Fig. 2 .

 12 Fig. 1. Schematic description of a condensing tumble dryer. Temperature sensors are indicated.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Variation of the leakage ratio at different external airflows and power supplies to

Fig. 5 .]

 5 Fig. 5. Leakage ratio and humidity of the internal airflow exiting the drum, plotted

Table 1 .

 1 Experimental design levels of the factors.

	c p	specific heat capacity	[kJ/kg°C]
	h	enthalpy	[kJ/kg]
	h 0	evaporation enthalpy, 0°C [kJ/kg]
	L V	leakage of water vapour [kg]
	m	mass	[kg]
	m &	mass flow	[kg/s]
	Q tot	total energy supply	[kJ]
	Q &	heat transfer	[W]
	SMER	specific moisture extraction
		rate	[g/kJ]
	T	temperature	[°C]
	V &	volume flow	[m 3 /s]
	Y ρ	humidity density	[kg/kg] [kg/m 3 ]
	Subscripts
	A	air
	C	condensate
	cover	outer cover of the dryer
	E	external
	f	between fan and heat exchanger (internal system)
	h	between heater and drum (internal system)
	hx	between heat exchanger and heater (internal system)
	HX	heat exchanger external airflow (external system)
	I	internal
	i	inlet
	o	outlet
	V	vapour
	W	water

Table 2 .

 2 Tests performed in the condensing tumble dryer with varying values of power supply to the heater, internal airflow and external airflow. The measured values of SMER and leakage ratio are presented.

	Experiment		Factors		Responses
	number	h [W] Q &	I V & [m 3 /h]	V & E [m 3 /h]	SMER [g /kJ]	L V [%]
	1	1355	66	72	0.259	50.1
	2	1666	66	72	0.264	49.7
	3	1329	88	72	0.257	56.3
	4	1606	88	72	0.265	54.2
	5	1381	66	155	0.241	29.3
	6	1673	66	155	0.248	30.3
	7	1401	88	155	0.241	35.8
	8	1660	88	155	0.251	34.2
	9	1381	77	113	0.253	38.8
	10	1617	77	113	0.257	37.4
	11	1500	66	113	0.249	32.1
	12	1521	88	113	0.253	42.4
	13	1578	77	72	0.264	46.4
	14	1510	77	155	0.243	30.7
	15	1442	77	113	0.251	38.0
	16	1516	77	113	0.251	37.7
	17	1529	77	113	0.251	38.1
	18	1575	77	113	0.256	35.2
	19	1523	77	113	0.252	36.2

& & & & & & & & & & & &(3)In this investigation, 19 test runs were made including five standard reference experiments.All tests were performed with 4 kg of dry cotton (conditioned in room air at 13 °C with the air relative humidity at 31%) wetted to a moisture content of 60% (db). The weight of the drying load was registered before and after each test run. The weight of the condensate was also registered.Temperatures of the air in the internal system were measured every second during the process. Mean values from ten seconds were registered. Temperature sensors with an accuracy of ± 0.5 °C were placed between the heater and the drying drum, T h , next to the fan that transports the internal airflow, T f , and between the heat exchanger and the

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