Charles Figuières

Solenn Leplay

Estelle Midler

Sophie Thoyer

The REDD scheme to curb deforestation: an ill-defined system of incentives?

The need to find a global agreement to limit deforestation has led to the REDD scheme which proposes that developed countries pay developing countries for CO2 emissions saved through avoided deforestation and degradation. This chapter describes the issues at stake and demonstrates with a stylized transfer scheme which describes the negotiation between developing countries over the allocation of the forest fund, that the REDD mechanism may induce perverse effects, higher contributions from the North leading in fact to greater deforestation rates.

Introduction

Safeguarding the tropical rainforest is one of the most important challenges for the future: about 13 million hectares of forest have been cleared each year between 1990 and 2005, mostly under the pressure of logging activities and agricultural land expansion (FAO, 2005).

Tropical forests provide local public benefits for almost 750 millions of people (CHOMITZ, 2007), regulating local climate, quality and quantity of water in watersheds, and preserving soil fertility. But their environmental benefits extend well beyond tropical forest countries. They are the second biggest stock of carbon on earth after oceans, therefore contributing to mitigate climate change. They are also the largest hotspots of terrestrial biodiversity, sheltering between 50 and 90 per cent of the total biodiversity of the planet (WCED, 1987). Deforestation has therefore huge environmental consequences at the world level: forest clearance is now the second leading cause of carbon emissions, just behind the energy sector, and is responsible for the extinction of many species. Consequently the preservation of tropical forests became a global issue and is now a hot topic on the agenda of international environmental negotiations, especially the United Nations Framework Convention on Climate Change (UNFCCC) and the Convention on biological diversity (CBD). At stake is an agreement between developed countries (or donor countries) which are willing to contribute to an incentive scheme to reduce the global deforestation rate, and tropical forest countries (or host countries) for whom limiting deforestation has an opportunity cost in terms of agricultural production and foreign exchange earnings from wood exports.

A transfer scheme is currently under examination: the United Nations program on Reducing Emissions from Deforestation and Degradation (REDD) proposes that developed countries pay developing countries for CO2 emissions saved through avoided deforestation. The REED scheme, as defined by the 2007 Bali meeting of the UNFCCC, is thus an output-based payment, financed by donor countries, and compensating for a stock service provided by tropical forest countries. However, there is no consensus yet on the way such financial incentives should be calculated and allocated. The Bali roadmap is thus encouraging parties to explore the feasibility of various transfer mechanisms, with the view to implement REDD after 2012 in the next commitment period of the Kyoto Protocol.

Most available analysis focus on a mechanism in which the compensation is paid proportionally to the difference between the observed rate of deforestation and a given baseline. The goal of the present work is to analyse whether such a proposal can effectively lead to a successful outcome, in which developed countries will accept to contribute to a global fund and developing countries will lower their deforestation below an agreed rate.

The article is organized as follows. The next section gives a short historical perspective about international negotiations on deforestation and summarizes the main contributions of economic theory to the debate. Section 3 constructs a simple framework where the north-south dimension of the deforestation dilemma can be captured. That section uses this framework to investigate the logic of the REDD compensation scheme and to assess whether such mechanism can be effective. It shows that the properties of such scheme are very disappointing and can in fact lead to a non cooperative outcome without any gains in terms of avoided deforestation. The conditions under which the scheme could work are restrictive and require that countries be perfectly informed about their preferences and costs, which is not credible. The last section concludes.

The genesis of REDD: a brief historical perspective

Developed countries have long been aware of the alarming rate at which deforestation is taking place in tropical countries and of the irreversible losses associated with the destruction of the primary forest. However, although several attempts have been made to establish a multilateral convention on forest protection, developing countries, represented by the G77, have been reluctant to make commitments which jeopardize their rights to exploit their forestry resources without compensations from the rest of the world. The 1992 Rio summit failed to launch such a convention. Since then, the only outcome of international negotiations has been the adoption of non-legally binding principles concerning sustainable forest management and trade of tropical timber.

The failure to reach a global agreement has been however partially compensated by other types of initiatives, mainly driven by biodiversity conservation concerns: there are a few examples of bilateral agreements in which a donor country finances the protection of a specific forest area in a host country; the CBD has also promoted a protected area policy, financed through the Global Environment Facility1 . In both cases, it is a project-based approach, in which donor countries only pay for incremental costs of protection in a given area: they are willing to compensate the operational costs of conservation, as well as a proportion of foregone revenues from land uses other than conservation, for the forest protection measures that would not have been undertaken otherwise by recipient countries. Although this approach -based on the principle of additionality-supposedly satisfies the individual participation constraints of tropical forest countries, it has been limited in scope (DEKE 2004), due to cumbersome control and administrative procedures and to the insufficient financial resources of the GEF which depends on voluntary contributions of developed countries.

The climate negotiations also failed to include deforestation in the 1997 Kyoto protocol. Although reforestation and afforestation projects were made eligible as carbon sinks projects and could thus be included in the Clean Development Mechanism2 , the deforestation issue was left aside. The main concerns was that forestry activities would crowd-out other -longer term-mitigation efforts and that leakage (the displacement of deforestation activities outside the project boundaries, without any net gan in the national deforestation rate) would be almost impossible to control and prevent.

The urgency of the climate change issue has led to the REDD proposal, tabled in March 2005 by the Rainforest Coalition in the 11th Conference of Parties of the UNFCCC.

The main innovation of REDD is to shift away from a logic of cost compensation towards a logic of purchase of CO2 storage service. Until then, all transfers were input-based payments, financing implementation costs of forest conservation. The REDD transfers are output-based payments: they are allocated per unit of real reduction of deforestation rate (compared to a reference rate, called the baseline) and the per-unit payment should reflect the market price of carbon emissions rather than the individual countries' conservation costs [START_REF] Deke | Financing National Protected Area Networks Internationally -The Global Environment Facility as a Multilateral Mechanism Transfer[END_REF] . Moreover, in contrast to CDM projects, the recipient countries retain full sovereignty over how to achieve the reduction in deforestation rate.The reward could either be direct monetary transfers from a multilateral fund financed by developed countries, or could be the issuance of internationally tradable emission allowances, fungible on the Kyoto market or on a separate permit market.

The REDD proposal is currently under examination and is triggering hot debates on the best way to design the transfers and make the scheme effective. The discussions cover a wide range of issues, from the risk of non permanence of forest carbon sinks (if forests are destroyed after the payments have been made) to the recurrent problem of leakage, at the international scale [START_REF]Global Forest Resources Assessment[END_REF] . The most difficult issues are however to overcome free-riding by donor countries, and to find an agreement on the mode of calculation of the baseline (TACCONI, 2009). These two issues are closely interlinked. The definition of the baseline will influence decision-making in both host and donor countries, through the calculations of the transfers obtained by host countries, the size of total contributions to be made by donor countries and the net gains in terms of avoided deforestation. If host countries succeed in negotiating high baselines, they will obtain large transfers without providing much effort in terms of avoided deforestation. On the other hand, too low a baseline will deter participation by host countries (KARSENTY and PIRARD, 2007). Parties and research institutions have submitted different proposals for the methodology of the baseline calculation: the historical baseline would reflect past trends of deforestation rates, at the individual level or at the global level, or a mix of both; the business-as-usual (BAU) baseline would be calculated on the basis of the deforestation rate that would occur without the implementation of REDD. Whereas the latter method can end up in endless controversies about the methodology to establish predicted scenarios of deforestation, the former approach penalizes countries with low past rates of deforestation and overlooks the "forest transition' phenomenon [START_REF] Karsenty | Changement climatique : faut-il récompenser la déforestation évitée ?[END_REF] . Despite the numerous proposals put on the negotiation table, no agreement has been reached on the baseline calculation method so far. The first explanation could be that countries have diverging views on the criteria that should justify international transfers: whereas some countries argue that transfers should "punish" past bad behavior, even at the expense of efficiency, others want transfer payments that deter future threats of pollution by offering greater compensation to countries with greater nuisance capacity. Another more fundamental reason is that the baseline calculation is a key element in the negotiation strategies of host countries, who are are aware that they will have to share between them the funds made available by donor countries to limit deforestation. The discussions about the baseline are to some extent comparable to a bargaining game for sharing a new resource.

In the vast theoretical literature on international environmental agreements, a few papers focus on the transfer schemes between donor countries wishing to conserve resources (such as biodiversity or tropical forest) with global public benefits, and recipient countries which have sovereignty over these resources. Donor countries -often developed countries -have to decide on their individual contributions to the multilateral fund, whereas recipient countries have to decide on their participation in the scheme and on the relative effort provided by each in the total conservation effort. The division between developed countries and developing countries of the net surplus generated by the cooperation is also at stake. BARRETT (1994) focuses on the free-rider problem in the contribution game to a global biodiversity conservation fund by developed countries. He shows that when a self-enforcing full cooperative agreement is attainable, then the net benefits are small compared to the non cooperative outcome. NEUMAYER (2001) summarizes this finding by stating that "cooperation is either narrow (instead of wide) or shallow (instead of deep)". However, Barrett's model, like most models on international cooperation, overlooks the potentially strategic behaviour of developing countries in the transfer game. RUPERT et al (2004) build a biodiversity bargaining game in which developing countries act strategically to extract more surplus from donor countries: they show that badly-designed institutions can in fact engender perverse effects which reduce biodiversity conservation instead of stimulating it.

We use a similar approach to build a stylized model of the North-South negotiation over the implementation of the REDD scheme in which the developed countries' decisions are their financial contributions to the global fund and the developing countries' strategic decisions are their individual deforestation rate and their individual baselines. We show that this mechanism can be effective, though in a very particular way defined by a specific threshold: under a given size of total contributions by the North, the mechanism has no impact of deforestation. Beyond that threshold, additional funding is counter-productive in that it increases deforestation! Overall, the present analysis does not make a strong case in favor of the REDD scheme.

Deforestation decisions in the South

Consider 2 countries in the developing South (labelled country 1,2) with a high endowment of forests. The North has no forest but it can decide to contribute to a global transfer fund which is used to pay rewards to developing countries accepting to reduce their deforestation [START_REF] Karsenty | Changement climatique : faut-il récompenser la déforestation évitée ?[END_REF] Advocates of the forest transition phenomenon argue that high rates of deforestation are only transitory and should decline with income growth, as demonstrated empirically by the Kuznets curve analysis for deforestation (KOOP and TOLE, 1999). Thus if it is expected that the rate of deforestation decreases naturally over time (KARSENTY and PIRARD, 2007), this should be taken into account in the revision of the baseline to avoid unnecessary monetary compensations. rates under a given individual baseline. Assume that the size of the global transfer fund is set and known by developing countries. The focus is on the deforestation decisions in the South, d i ∈ 0, d i , i = 1, 2, where d i is an exogeneous constant, presumably the total hectares of forest in country i. Let (d 1 , d 2 ), be the vector of deforestation decisions.

Countries' preferences in the South are captured by utility functions u i (c i ), defined over a composite consumption good c i . Those utility functions are strictly increasing and concave, u i (c i ) ≤ 0 < u i (c i ). The composite good is produced via a technology that uses two inputs: deforestation d i and an initial exogenous wealth w i which can be increased by transfers T i from the North.Thus:

c i = f i (d i , w i + T i ) .
The production functions are increasing and concave with respect to each argument, that is

f i 1 = ∂f i ∂d i > 0, f i 2 = ∂f i ∂ (w i + T i ) > 0, f i 11 = ∂ 2 f i (∂d i ) 2 ≤ 0, f i 22 = ∂ 2 f i [∂ (w i + T i )] 2 ≤ 0.
Plugging back those technological constraints into utility functions u i , we can redefine the cardinal representation of preferences as follows:

U i (d i , w i + T i ) ≡ u i f i (d i , w i + T i ) ,
where U i is increasing and concave with respect to both arguments. This simple model captures some of the logic underlying the North-South deforestation dilemma: southern countries can enjoy the same level (or a higher level?) of utility after limiting deforestation, provided their sacrifice is offset by a sufficient increase of the second input, i.e. by monetary transfers. Utility functions are specified as follows [START_REF] Karsenty | The architecture of proposed REDD schemes after Bali: facing critical choices[END_REF] :

U i (d i , w i + T i ) = α i log(d i ) + β i log(w i + T i ), α i , β i > 0.
We assume thus that developing countries, when negotiating, do not take into account the global level of deforestation and its impact on climate change. Accordingly in the model the global public good role of forests does not appear in utility functions of the South [START_REF] Koop | Is There an Environmental Kuznets Curve for Deforestation?[END_REF] .

The mechanism under consideration subsidizes developing countries that are willing to lower their deforestation compared to a baseline level d b i . Formally:

T i = t d b i -d i if d i < d b i 0 otherwise
In the expression above, t is the exogenous unitary price of one hectare of forest saved under the mechanism, or alternatively the exogenous price of equivalent tons of CO 2 on the carbon [START_REF] Karsenty | The architecture of proposed REDD schemes after Bali: facing critical choices[END_REF] Getting back to the original formulation, we could assume for instance that:

u i (c i ) = c i ,
and f i (d i , w i + T i ) = α i log(d i ) + β i log(w i + T i ), α i , β i > 0, i = 1, 2.
market. Clearly, when the mechanism is implemented, the baseline operates as a ceiling. The budget of the global transfer fund must balance. Therefore, if the sum of the North contributions to the fund is e then:

T 1 + T 2 = e
Under the laisser-faire scenario, there is no monetary tranfers (T 1 = T 2 = e = 0) and southern countries settle for decisions d N i implying maximal deforestation. Indeed:

U i 1 (d i , w i ) = α i d i > 0 ⇒ d N i = d i .
Such global deforestation level d 1 + d 2 is judged to be too high by the North, which is thus prepared to compensate the South for limiting it.

We assume that the timing of decisions in the South runs as follows: 1) developing countries bargain over the baseline knowing the size of the global transfer fund e and knowing the per unit "price" for avoided deforestation t, 2) developing countries choose independently their deforestation rates. We solve the model by backward induction.

Deforestation decisions

In the last decision period, developing countries maximize their utility through their choices of the level of deforestation under the REDD mechanism, knowing their baseline d b i that has been determined in the previous period. In the following, we focus on the solution di of the utility maximization when di < d b i . To ensure this, assume parameters are such that, for the prevailing price t and the observed baseline

d b 1 , d b 2 : Condition 1 α i w i < β i td b i ,
and

Condition 2 α i log α i α i +β i w i t + α i α i +β i d b i +β i log β i α i +β i w i + α i t α i +β i d b i > α i log d i +β i log (w i ) .
Then, country i's utility, as a function of d i , is depicted in Figure 1. It has a discontinuity point at d i = d b i ; condition 1 entails that the slope of the utility function is negative when d i approaches d b i from below; given that this fonction has a positive slope and that it is concave in the interval 0, d b i , necessarily there exists a value di that cancels out the derivative of U i . And condition 2 ensures that the utility computed at the interior value di is larger than the utility computed at the upper corner d i . Formally, optimal deforestation decisions then solve:

U i 1 (d i , w i + T i ) -tU i 2 (d i , w i + T i ) = 0, ⇒ α i d i - β i t w i + T i = 0. ⇒ di = d i d b i ≡ α i α i + β i w i t + α i α i + β i d b i .
At such an equilibrium:

∂ di ∂t = - α i α i + β i w i t 2 < 0,
which means, as expected, that the larger the exogenous price t, the lower the deforestation at equilibrium. Moreover we have:

0 < ∂ di ∂d b i = α i α i + β i < 1.
This result indicates that country i s deforestation increases, but less than proportionally, with the baseline level d b i that is negotiated in the first stage.

d i i d ɶ (e) b i d i d U i (d i ,w i +T i ) U i ( i d ,w i )

Bargaining over the baseline in the South

In the first period, developing countries anticipate the second period decisions described above.

Their indirect utility functions are:

H i (d b i ) ≡ U i [d i (d b i ), w i + t d b i -d i (d b i ) ].
The bargaining over the baseline can be conceptualized in several ways. Whatever the chosen bargaining protocol, developing countries know that they cannot claim more than what is available in the global transfer fund e. Hence, the outcome of the bargaining situation db 1 , db 2 must belong to the following set:

Ω = d b 1 , d b 2 / e t = 2 i=1 (d b i -d i (d b i )), d b i ≤ d i , i = 1, 2 .
If developing countries fail to reach an agreement, the North will refuse to make any transfer.

In such an event, deforestation is at its maximum rate and utilities are:

H i ≡ α i log(d i ) + β i log(w i ).
Assuming that the bargained outcome is given by the Nash solution, then H 1 , H 2 play the role of threat points for country 1 and country 2.

And db 1 , db 2 solve:

max (d b 1 ,d b 2 )∈Ω (H 1 (d b 1 ) -H 1 ε 1 H 2 (d b 2 ) -H 2 ε 2 ,
where ε i represents country i's bargaining power, ε 1 , ε 2 ≥ 0, and

ε 1 + ε 2 = 1.
To simplify the calculations, let's assume that, although developing countries may have different bargaining powers ε i , different initial wealth w i and heterogenous forest endowments d i , they share the same utility parameters, that is:

α i = α , β i = β , i = 1, 2.
In the perspective of the present paper, there are two crucial questions: i) what is the effect of the size of the global transfer fund on the endogenous baselines? and more importantly, ii) what is the effect of e on deforestation decisions? We can establish the following answers:

Proposition Starting from a level of transfer that sustains an interior optimum for deforestation decisions, the higher the size of the global transfer fund e, the greater the agreed baselines and the larger the deforestation rates.

Proof. From the constraint in Ω, one can calculate d b 2 as a function of d b 1 and e :

d b 2 d b 1 ; e = e t -d b 1 + d 1 (d b 1 ) + α α + β w 2 t α + β β
The bargaining problem can then be rewritten as a single decision variable problem

max d b 1 (H 1 (d b 1 ) -H 1 ε 1 H 2 (d b 2 d b 1 ; e ) -H 2 ε 2 ,
where

d b 1 is chosen so that d b 1 , d b 2 d b 1 ; e ∈ Ω.
The first order condition is:

ε 1 (H 1 (d b 1 ) -H 1 ε 1 -1 H 2 (d b 2 d b 1 ; e ) -H 2 ε 2 H 1 (d b 1 ) +ε 2 (H 1 (d b 1 ) -H 1 ε 1 H 2 (d b 2 d b 1 ; e ) -H 2 ε 2 -1 H 2 (d b 2 d b 1 ; e ) ∂ ∂d b 1 d b 2 d b 1 ; e = 0. (1)
This equation implicitly defines d b 1 as a function of e. Using the implicit function theorem, after some calculus and rearrangements one finds (see appendix):

∂d b 1 ∂e > 0 (2)
And from the definition of d 1 (d b 1 ) :

∂d 1 ∂e = α α + β ∂d b 1 ∂e > 0. (3)
The same reasoning applies to the second decision variable, d 2 , which completes the proof. Therefore, under the reasonable assumptions made so far, an increase in the total contributions from the North to the global fund increases the level of deforestation chosen by developing countries! The mechanism implements a wrong incentive program: instead of fostering deforestation reduction, it induces developing countries to increase their level of deforestation and still gain positive transfers. This result, striking at first sight, is rather intuitive upon reflection. An increase in the size of the global fund is matched by an increase in negotiated baselines because developing countries interpret it as a greater pie to share. This leaves room for an increase of deforestation, provided it is not too large compared to the increment of the baseline, in order to get a strictly positive transfer T 1 . Expression (3) shows that this is the case because 0 < ∂d 1 ∂e < ∂d b 1 ∂e . To put it another way, there is a pernicious effect that stems from the endogenous adjustment of the baselines.

As regards contributions to the global transfer fund, the North therefore has incentives to downsize them in order to limit the temptation by developing countries to negotiate higher baselines. From the above proposition, this will reduce the baselines and the optimal deforestation decisions in the South. The utility levels attained at the negotiated baselines

H i (d b i ) = α i log α i α i + β i w i t + α i α i + β i d b i + β i log β i α i + β i w i + α i t α i + β i d b i
will also be reduced.

There exists a specific level of contributions e, and the corresponding baselines

d b 1 , d b 2
, such that for any lower size of the global transfer fund, developing countries will prefer to give up transfers and will choose their maximal deforestation rates. These threshold baselines are those that violate condition 2; they equalize the utility level at an interior solution with the utility level at the upper corner (see Figures 2 and3). They are defined as the solution to: .

H i = U i [d i (d b i ), w i + t d b i -d i (d b i ) ], i = 1, 2 or
α i log(d i ) + β i log(w i ) = α i log α i α i + β i w i t + α i α i + β i d b i +β i log β i α i + β i w i + α i t α i + β i d b i . (4)
What the analysis of the present paper reveals is that there is no point for the North to offer contributions larger than e, for this will increase deforestation (and will cost more). Neither should it provide a smaller transfer fund than e, since deforestation rates in the South would then rocket to their maximum levels. Differently stated, the mechanism is either ineffective, or it implies a waste of resources, except at e. In practice, identifying this threshold is no simple matter, in particular because it depends on utility parameters α and β (see expression 4) which are not readily observable.

d i b i d i d U i (d i ,w i +T i ) i d ɶ ( e) U i ( i d ,w i ) U i when e e =

Conclusion

This stylised model shows that a transfer mechanism based on an endogenous baseline can engender perverse incentives: although it is designed to counteract deforestation, it creates incentives for developing countries to negotiate greater baselines, therefore allowing them potentially to both increase their deforestation rates and obtain positive transfers. Of course, the outcome of such scheme should be the refusal of developed countries to contribute significantly to the global transfer fund. This result is independent of the preference and the relative bargaining power of developing countries. It raises serious concerns about the efficiency of the REDD mechanism and its capacity to sustain a cooperative outcome. It provides arguments therefore to conduct a more careful analysis of the way the negotiation is conducted during the different decision phases of the REDD implementation, namely: the rules under which contributions by developed countries to the global forest fund will be calculated; the negotiations over the rules defining the baseline calculations.

Of course this result is related to our modelling choice. The strongest assumption in this model is that developing countries negotiate over their respective baselines without any intervention from the North. This can seem hardly credible in the first place. However, the on-going discussions over the REDD scheme tend to confirm this modelling option: if the international community succeeds in creating a global transfer fund for the financing of REDD, rules will be established to decide upon the Northern countries' contributions. Developing countries will then be able to assess the size of this fund and they will negotiate over the sharing rules of these new financial resources. It is not unreasonable to assume that the main driver of the negotiation will be to obtain the largest potential share of the fund, and that developed countries won't have much influence in the negotiation (except by establishing the credible threat of not creating the fund) even if, as emphasized in section 2, rules can be justified by ethical, historical or efficiency criteria. This is already revealed by the strategic positions of Brazil and Indonesia, two large deforesting countries defending the adoption of an historical baseline system, as opposed to the positions of Costa Rica and countries of the Congo Basin, with past moderate deforestation rates, defending a BAU baseline.

This paper has chosen to model the REDD scheme as based on direct monetary transfers but results would be identical if transfers were made in the form of tradable permits, since the main limitation of the proposed scheme is the baseline system. We therefore suggest that an alternative system of transfer be examined which could be based for example on the stock of forest rather than on the deforestation rate itself.

Figure 1 :

 1 Figure 1: Utility Function

With those threshold baselines d b 1 , d b 2 ,e = t d b 1 -d 1 d b 1 + d b 2 -d 2 d b 2

 121122 one can compute the corresponding total monetary transfers e from the North:

Figure 2 :Figure 3 :

 23 Figure 2: Utility Function when e = ē

Appendix: Calcul of dd b 1 de 1 de 1 and ∂f ∂e : ∂f ∂d b 1 = [ H 1 2 (H 2 - 2 + H 1 (H 1 - 2 ∂d b 1 H 2 ]+ ( 1 - 2 ∂d b 1 + (H 1 - 2 ∂d b 1 H 2 ) 2 + (H 1 - 2 ∂d b 1 ) 2 H 2 ] 1 - 2 ∂e+ (H 1 -H1 ) ∂d b 2 ∂d b 1 ( 1 - 2 ∂e+ H 2 ∂d b 2 ∂e (H 2 -

 111122211212121121221212212211222 We choose to define f (d b 1 , e) as the function(1) given by the CPO condition. We use the implicit function theorem to find dd b . is the bargainig power of the country 1 and so the bargaining power of country 2 is (1 -). We study ∂f∂d b H2 ) 1-( -1)(H 1 -H1 ) -H1 ) -1 (H 2 -H2 ) 1- + (H 1 -H1 ) -1 H 1 (1 -)(H 2 -H2 ) -∂d b )[ (H 1 -H1 ) -1 (H 2 -H2 ) -H 1 H 2 ∂d b H1 ) (-)(H 2 -H2 ) --1 ( ∂d b H1 ) (H 2 -H2 ) -( ∂d bAnd so, under conditions 1 and 2, H1 )-1 H 1 (1 -)(H 2 -H2 ) -H 2 ∂d b )[-(H 2 -H2 ) --1 (H 2 ) 2 ∂d b H2 ) -]

The Global Environment Facility (GEF) is a global partnership among 178 countries, international institutions, non-governmental organizations and the private sector. It helps to finance sustainable development initiatives in the field of global environmental issues. It is also the designated financial mechanism for some multilateral environmental agreements and framework conventions.

the Clean Development Mechanism (CDM) allows developed countries -which must satisfy emission reduction targets -to use certified emission reductions obtained by financing specific projects in developing countries. Eligible projects include emission abatement projects as well as the replanting of new forests. Forest conservation projects are excluded.

[START_REF] Deke | Financing National Protected Area Networks Internationally -The Global Environment Facility as a Multilateral Mechanism Transfer[END_REF] Numerous research and expertise works have attempted to evaluate the unitary carbon price required to compensate the opportunity costs of avoided deforestation. LOISEL (2008) makes a review of these recently published evaluations and concludes that the price of carbon credits could vary from 0.06 to 730 euros per ton of CO2 stored in

forests.[START_REF]Global Forest Resources Assessment[END_REF] If several countries reduce their deforestation rates, the world market price of timber will increase, providing incentives for non signatory countries to increase logging.

A formulation that captures this role would have d j , j = i, as a third argument in the utility functions.


Climate change and the carbon balance of tropical rainforests

 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1997 1999 2001 2003
--

  55 [0.95; 1.98] + 0.50[-0.18; 0.96] + 1.52 [0.62; 2.15] + 0.76[-0.56; 1.31] + 0.34[-0.44; 0.77] -0.38[-1.68; 0.37] Rutishauser & Blanc: pers. comm. 15Annual above ground biomass balance in inventory plotsMean ≈ 0.71 Mg ha -1 y -1Net annual accumulation in aboveground biomass since 25 yearsOver AmazoniaHigh variability among sites, but a general trend for a net annual accumulation inaboveground biomass since 50 years in undisturbed forests in Amazonia Annual above ground biomass balance in inventory Influence of global climate changes on global carbon balance Hadley Centre for Climate Prediction and Research. The Met. Office. HadCM3 Expected change in average soil moisture content Lower soil water content (more frequent droughts) in the Amazon region Seasonal variations in rainfall at Guyaflux, French Guiana High seasonal variations in Net Ecosystem Exchange (C) Succession of periods of high storage (dry season) or high release of C (wet season) Influence of global climate changes on global carbon balance Saturation, or even a decrease of carbon sinks in tropical regions (America & Africa) Suggested explanation : related to the increase in temperature which will induce an increase in evaporation and then an increase in soil drought, leading to reduced photosynthesis ?? Not consistent with patterns observed at ecosystem level (stronger decrease in Reco as compared to GPP) Influence of climate changes on carbon sinks Conclusions Simulations of global climate changes for the tropical regions still imprecise o Need for better parameterization of models and long-term observations of climate and GHG fluxes in these regions (Picarro -Guyaflux) Whatever these changes, they will influence the functioning of tropical rainforest ecosystems, particularly gas exchange with atmosphere Potential impacts of more frequent and/or more severe droughts: • Change in forest dynamics (higher mortality rates) o Potential feedbacks ? More opened forests? More photosynthesis and growth? • Change in carbon balance o Lower or higher carbon storage during dry periods, depending on the influence on ecosystem respiration and photosynthesis? Past vegetation changes related to dry / wet periods during Pleistocene / Holocene occurred slowly and over long periods: o What will be the dynamics of these changes under fast climate changes? Thank you for your attention …

Net Ecosystem Exchange (NEE) obtained from eddyflux towersAdapted from Ometto et al. 2005

Friedlingstein & Dufresne 2000

Rutishauser et al. JVS in review

Annual above ground biomass balance in inventory plots

Biomass loss by mortality

Biomass gain by Tree growth and recruitment

Differences in balance between years and subplots are mainly explained by differences in mortality rates


Anne Thierry

Aroma compounds in dairy products

est destinée au dépôt

III International Symposium on Lactic Acid Bacteria Second Argentinean LAB net meeting

September 1517 2009 San Miguel de Tucumán -Tucumán, Argentina

Organised by

The Symposia on Lactic Acid Bacteria (LAB) organised by the Centro de Referencia para Lactobacilos (CERELACONICET) since 1996, represent a forum for interaction among different research groups from scientific and technological institutes and/or related companies in Argentina and Latin America.

Throughout the "III International Symposium of Lactic Acid Bacteria and II LAB Net" the advances reached during the last three years on basic and applied knowledge on LAB as well as the new trends on health and animal LAB applications will be dealt with. Topics will include basic studies on Physiology and Metabolism of LAB: genomics; metagenomics; microbiome; probiotics; bacteriocins and their applications; and use of LAB in the production of nutraceutics and as vectors for live vaccines. The exchange of knowledge among the different groups actively involved in all related areas of LAB is encouraged as well as the aggluttination of the companies interested to acquire the achieved advances.

On behalf of the Organizing Committee we are pleased to hereby inform you that the following speakers have confirmed their participation at the symposium:


Dr Pierre-Sylvain Mirade
email: mirade@clermont.inra.fr

CFD Prediction of the Air Velocity Field in Modern Meat Dryers

I. INTRODUCTION

No other technology results in such an aromatic and desired flavour of meat products as fermentation and drying [START_REF] V Kottke | Engineering aspects in fermentation of meat products[END_REF]. Dry sausages are one of the most important fermented meat products. In Europe, total production of non-smoked moulded dried sausages is about 350,000 tonnes a year, a significant proportion of which comes from southern European countries including Italy, Spain and France (90,000 tonnes a year). In northern European countries such as Germany, Denmark, Sweden and Norway, almost all dry sausages produced are smoked during processing. In Hungary, the traditional salami is even smoked in a first drying step, before being moulded in a second ripening step [START_REF] V Kottke | Engineering aspects in fermentation of meat products[END_REF].

In the successive operations involved in dry sausage manufacture, namely grinding of lean meat and fat, mixing with additives, stuffing in casings, and drying, the drying process is crucial. Indeed, to obtain a well-balanced drying of all sausages, airflow patterns and indoor climate (temperature and relative humidity) should be homogeneous throughout the drying room. In practice, water loss differences between sausages are observed in the dryer which result from local heterogeneities in the air velocity distribution. This problem is partially addressed through the rearrangement of the trolleys of sausages in the room during the drying process. Nevertheless, many authors have reported that poor control of drying conditions is the main raison for low quality [START_REF] Noel | Etude du processus de séchage des saucissons en vue d'éviter le croûtage, accident de fabrication préjudiciable à la qualité[END_REF][START_REF] Dabin | Le Saucisson Sec[END_REF]. During drying, the water content of the sausages should decrease homogeneously. When the rate of water evaporation from the surface of the sausage is higher than the rate of water migration from inside the sausage, a dry crust (also called "dry rim") is formed which adversely affects sausage texture and flavour; conversely, when the evaporation rate is lower, the surface remains too moist, which favours the growth of undesirable moulds that can impair product texture, flavour and safety. Hence, the drying process consists in continuously fitting the drying rate to a product undergoing perpetual biochemical and biological evolution, and maintaining water activity at the product surface at an ideal value in order to develop the desirable flora. In other words, ripening has an influence over the main physical, chemical and microbiological transformations that take place inside the products and which define the final organoleptic properties of dried products. As water exchanges at the product surface are directly related to the characteristics of the surrounding air (temperature, velocity and relative humidity), it is of paramount importance to identify global airflow patterns inside the dryer.

In Europe, dry sausage and especially ham were originally manufactured in mountainous highlands, since the outside air could be used inside the meat dryers all almost year round without conditioning, due to the fresh temperature and high relative humidity. More recently, static dryers equipped with cooling batteries level with the ceiling and heating batteries level with the floor have appeared in geographic areas with a less favourable natural climate. They operate by mixing descending fresh air volumes with ascending hot air volumes, thus generating natural ventilation with very low air velocity.

Hygrometric control was achieved by condensation of water on the cooling batteries. This type of meat dryer was used to manufacture hams and low-diameter dry sausages [START_REF] Dabin | Le Saucisson Sec[END_REF]. To reduce ripening time, fans were introduced into the meat dryers to force air to circulate around the products at a velocity of 0.1 m.s -1 . At the very beginning, blowing ducts were placed level with the floor while suction ducts were placed level with the ceiling. Although the direction of air movement could be inverted in this type of dryer, heterogeneity in air distribution remained in the full volume filled with the products, causing strong heterogeneity in drying between the upper and lower part, thus compelling professionals to regularly move their products. To even out the drying conditions, and thereby product processing, throughout the entire volume of the plant, modern meat dryers were created where air distribution was time-dependent. This chapter reports on scientific studies aimed at analysing the significance and effects of the specific operation of modern meat dryers through numerical modelling, with particular emphasis on dryers of large height which are currently increasingly used in industry.

II. OPERATION OF MODERN MEAT DRYERS

Figure 1 shows the layout of a typical modern meat dryer with a schematic description of the airflow pattern. The geometry of this type of meat dryer is simple; the airflow is generally supplied through two stainless steel ducts of rectangular cross-section fitted with plastic conical jets placed on each side of the plant, and is extracted level with the ceiling by means of two or three stainless steel ducts fitted with adjustable plastic extraction apertures. These modern meat dryers are characterized by a main upward airflow generated by two downstream airflows generated by conical jets which merge over the plant floor. As indicated earlier, when attempting to create homogenous drying conditions throughout the entire volume of a plant, it is important to take into account the fact that the operation of a modern meat dryer is time-dependent, and this for two reasons.

Firstly, as regards air distribution, the airflow supplied by two lateral blower ducts ranges from a high to a low rate in the first duct in a few tens of seconds while it reciprocally ranges from a low to a high rate in the second duct, thus giving rise to a periodic ventilation cycle (Figure 2). However, the overall blower airflow rate remains steady at any given time, at 100%. Figure 2 highlights that the ventilation cycle has a sinusoidal form, since the distribution of airflow rate in the two blower ducts is generally set by adjusting a regulation valve placed on the duct supplying air to the two blower ducts. The two inlet airflows are then directed downstream, descending along the lateral room walls before merging over the floor in a location that depends on the value of the ventilation cycle. The more unbalanced the ventilation cycle, the more distant the location of the merging area from the middle of the dryer. Once merged, the airflow then moves upward towards the extraction ducts, at the same time bathing the meat products filling the plant and exchanging heat and moisture with them. This ventilation cycle means that the merging location of the upward airflow moves cyclically over the drying floor. All meat products are consequently bathed by the same airflow during full periods of the ventilation cycle, and a priori are thus dried in a homogeneous way. Furthermore, during ventilation, air velocity ranges from 5 to 20 m.s -1 at the output of the conical jets of the blower ducts, and is on average 0.4 m.s -1 around the products.

Secondly, the specific ventilation pattern previously described and which is intended to supply air to the dryer alternates rapidly with a rest sequence in which there is no ventilation, depending on the level of relative humidity in the volume filled with the products; this relative humidity increases due to water evaporating from the surface of the sausages. Ventilation is reactivated once a high level of relative humidity is reached, in order to reduce relative humidity until a low level is reached. Periods of ventilation generally correspond to around 1/3 of total ripening time (Figure 3).

A modern meat dryer therefore works by a series of ventilation cycles and rest sequences (Figure 3) managed by an operator who generally uses empirical rules to adjust the drying conditions. In practice, these rules are known to be affected by the design (dimensions, location of the blower and extraction ducts, etc.), and filling level of the dryer, as well as by the amplitude of the ventilation cycle. In other words, both the design of modern meat dryers and the optimal process conditions are based more on the practical experience accumulated by plant designers and dried meat manufacturers over the years than on the results of academic research.

III. AIR VELOCITY FIELDS IN MODERN MEAT DRYERS

The majority of research on the processing of dried sausages or hams reported in the literature deals with fermentation, transfers from inside the product, or drying kinetics as a function of air properties [START_REF] V Kottke | Engineering aspects in fermentation of meat products[END_REF][START_REF] Lenges | Etude des processus de séchage des saucissons[END_REF][START_REF] Baldini | Détermination de l'activité de l'eau a w des produits ensachés crus en fonction de la teneur en eau[END_REF][START_REF] Stiebing | Influence of the pH on the drying pattern in dry sausage[END_REF][START_REF] Lucke | Starter cultures for dry sausages and raw ham[END_REF][START_REF] Jd Daudin | Water and salt transfers analysis in drying of sausages[END_REF][START_REF] Baldini | Dry sausages ripening: influence of thermohygrometric conditions on microbiological, chemical and physico-chemical characteristics[END_REF][START_REF] Bolumar | Acidity, proteolysis and lipolysis changes in rapid-cured fermented sausage dried at different temperatures[END_REF][START_REF] Ai Andrés | Sensory characteristics of Iberian ham: influence of salt content and processing conditions[END_REF]. For example, Daudin, Kondjoyan and Sirami [START_REF] Jd Daudin | Water and salt transfers analysis in drying of sausages[END_REF] highlighted steep gradients in water content in the first 10 mm close to the surface of drying sausages; they also indicated that accurate control of the air characteristics around the sausages was essential in order to control water activity at the sausage surface [START_REF] Jd Daudin | Water and salt transfers analysis in drying of sausages[END_REF].

A. Experimental Investigation

There are few experimental and numerical studies available on the overall operation of modern meat dryers [START_REF] Ps Mirade | Analyse expérimentale de l'aéraulique d'un séchoir à saucisson[END_REF][START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF][START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. Experimental analyses carried out in modern meat dryers are understandably rare since the measurements are particularly laborious and time-intensive due to the natural unsteadiness of the airflows and especially the ventilation cycle which continuously modifies the air velocities at the output of the conical jets. The only method that can be used to measure air velocities in this kind of plant is the standard average procedure that consists in averaging velocity measurements over a sufficiently long length of time (over one or several ventilation cycles at each measurement point) to obtain a constant value for mean velocity [START_REF] Ps Mirade | Analyse expérimentale de l'aéraulique d'un séchoir à saucisson[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF].

In a 134 m 3 small-scale sausage dryer filled with 108 objects made of polystyrene (1.70 m x 0.25 m x 0.15 m) arranged in 6 rows in order to reproduce industrial filling levels, Mirade and Daudin [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF] measured air velocity distribution in five configurations, corresponding to two different steady distributions of the ventilation cycle, namely 50%/50% and 20%/80% per blower duct. The first airflow distribution gave a large area with air velocities reaching 2 m.s -1 in the middle of the dryer, but a wider airflow than expected as a result of slow and slight time-variations in the blower airflow rate from each duct. Moreover, the authors noted that changing the distribution of the airflow rate from 50%/50% to 20%/80% completely disrupted airflow patterns, with the appearance of a poorly ventilated area at the centre of the dryer and air velocities of about 1.5 m.s -1 close to the blower ducts. In the 20%/80% configuration, the authors concluded that the large airflow blown in from the right-hand side duct to the floor moved along the floor and up the opposite wall, drawing in the airflow from the left-hand side duct.

B. Steady-state Numerical Investigation

Numerical studies of airflows in modern meat dryers have often been performed using CFD techniques.

With the development of cheaper, more powerful computers and commercial packages, over the years CFD has been increasingly applied to assess airflow patterns in modern meat dryers [START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF][START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF], ever since the pioneering studies performed by EDF, the French producer of electricity, and cited by Dabin and Jussiaux [START_REF] Dabin | Le Saucisson Sec[END_REF], that aimed to optimize air circulation inside the drying room in order to obtain more regular product-drying.

P.S. Mirade

From two calculations using steady-state boundary conditions and corresponding to two different distributions of airflow rate between the two blower ducts of the room (50%/50% and 30%/70%), these original studies indicated a complex air circulation pattern including two swirls that shifted laterally as a function of the air distribution between the two blower ducts. Consequently, the velocities of air in contact with dried sausages ranged from 0.4 m.s -1 to 0.6 m.s -1 , and were threefold to fivefold higher than the theoretical velocity determined from the total airflow rate blown in the room divided by its surface [START_REF] Dabin | Le Saucisson Sec[END_REF].

A similar approach, namely three steady-state and two-dimensional CFD simulations corresponding to airflow rate distributions between the two blower ducts of 50%/50%, 59%/41% and 67%/33%, respectively, identified a strong heterogeneity in airflow pattern in a salami dryer, with air velocities ranging from 0.2 to 0.8 m.s -1 in the volume filled with the products [START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF].

The heterogeneity in air velocity magnitudes in the volume filled with the products was confirmed by 3D numerical results obtained by Mirade and Daudin [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF] using the commercially-available CFD code Star-CD [START_REF]Star-CD Manuals[END_REF], in the case of a 134 m 3 small-scale sausage dryer, for two steady-state ventilation cycle configurations between the two blower ducts (50%/50% and 20%/80%). Calculations were made on a Sun Sparc 10/41 workstation with 128 Mo of RAM. Airflow was considered as steady, incompressible and isothermal. Main flow turbulence was taken into account using the tried and tested k-ε model [START_REF] Be Launder | Mathematical Models of Turbulence[END_REF] when far from the walls -which were assumed to be smooth -and where the standard wall function was applied [START_REF] Hirsch | Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows[END_REF]. Even though the k-ε model is known to perform poorly in a variety of important cases, such as some unconfined flows or flows with large extra strains, it is currently widely used for turbulence modelling since it is robust, time-efficient and fairly accurate. The SIMPLE algorithm [START_REF] Sv Patankar | A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows[END_REF] was chosen for coupling pressure and velocity and to introduce pressure into the continuity equation. A first-order upwind differencing scheme was incorporated into the computational model as discretization scheme for the convection terms of each governing equation. First-order schemes are known to increase numerical diffusion due to discretization errors, especially when the flow is not aligned with the grid [START_REF] Hirsch | Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows[END_REF]. Although they therefore yield less accurate results, first-order schemes give better convergence of calculation than second-order schemes. Complete convergence of the discretized differential equations ranged from 5 to 8 days, reaching 8 days when using 300,000 vertices for meshing the 134 m 3 small-scale sausage dryer [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF].

Figures 4a-b show the distribution of the simulated air velocity patterns according to a vertical section located approximately in the middle of the dryer, for inflow distributions of 50%/50% and 20%/80%, respectively [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF]. When the distribution of the airflow rate was balanced between the two blower ducts (50%/50%), calculations revealed that the higher air velocities were located level with the floor and in the middle of the dryer. On either side of this central area, poorly ventilated areas with air velocities lower than 0.6 m.s -1 were highlighted (Figure 4a). Conversely, unbalancing the distribution of the airflow rate from 50%/50% to 20%/80% completely disrupted the airflow patterns, as illustrated in Figure 4b, where the lower air velocities were concentrated in the middle of the dryer whereas the higher air velocities were found close to the two blower ducts.

Using 2D CFD modelling, Mirade and Daudin [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF] also highlighted a very unsteady airflow pattern when the airflow rate was closer to 50%/50%. An imbalance of only 4% between the left (54%) and the right-hand side (46%) blower duct greatly modified the location of the well-ventilated central area, which shifted over 60 cm towards the right, as indicated in Figure 4c, thus confirming the findings of the original studied carried out by EDF [START_REF] Dabin | Le Saucisson Sec[END_REF]. Furthermore, and again using the Star-CD code, Mirade and Daudin [START_REF] Ps Mirade | Etude numérique en 2 dimensions du cycle de ventilation d'un séchoir à saucisson moderne[END_REF] studied the effect of changes in airflow structure in relation to amplitude from 50%/50% to 10%/90% and dissymmetry of +/-5% in the ventilation cycle; it was assumed that the ventilation cycle was linear and that this non-steady-state problem (due to the ventilation cycle) could be numerically approached as a series of steady-state problems. By integrating the air velocities simulated between a low level and high level during one period of the ventilation cycle, they identified 60%/40% as the amplitude giving the most homogeneous airflow inside the area filled with the sausages, despite the fact that there was a gradient in air velocity distribution in relation to the height within the plant (Figure 5a). They also highlighted the need for controlled regulation of the ventilation cycle in modern meat dryers, since a slight variation of +/-5% in the airflow rate at a distribution of around 60%/40% markedly disrupted the airflow pattern, which became strongly dissymmetric (Figure 5b). On account of the simplicity of the system regulating and distributing airflow between the two blower ducts, and due to the marked unsteadiness of the airflow around the 50%/50% blower conditions, dysfunction in the ventilation cycle frequently occurs in industrial settings, leading to slight variations around the low and high levels with no change in the overall blower airflow rate. Hence, in practice, there is greater heterogeneity in sausage product treatment between different locations in the plant. Figure 5b indicates the appearance of a poorly ventilated area with velocities lower than 0.4 m.s -1 on the left-hand side of the sausage dryer, i.e. where the air velocities at the output of the conical jets were the highest. The slight variation in airflow rate distribution between the two blower ducts globally increased the air velocity gradients.

All these simulations were performed using the same modelling procedure as previously [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF], i.e. the kε model [START_REF] Be Launder | Mathematical Models of Turbulence[END_REF] for modelling turbulence, the SIMPLE algorithm [START_REF] Sv Patankar | A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows[END_REF] for coupling pressure and velocity, and a first-order upwind differencing scheme [START_REF] Hirsch | Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows[END_REF] as discretization scheme for the convection terms in the governing equations. Without using CFD, Rizzi [START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF] developed a parametric model to rapidly predict airflow velocity patterns in ascending flow ripening chambers, with the idea of improving the operation and design of these industrial plants by means of dynamic ripening simulation software coupling a fluid dynamics model to a numerical model of the sausage drying process. The fluid dynamics model was built to give the air velocity module as output and to give direction as a function of the geometrical characteristics of the drying chamber (dimensions, location of the blower and extracting ducts, number and location of the products loaded) and of the inlet airflow conditions (overall mass flow rate and inflow sharing ratio between the two blower ducts).

Several assumptions (incompressible fluid, steady and uniform motion) have been made in order to construct an accurate, flexible and computationally "light" fluid dynamics model. Moreover, the main idea upon which this model is based consisted in defining an imaginary 2D pipe network inside the drying room, thus assuming all parameters to be constant along the room depth. Once both geometrical and fluid dynamics parameters have been set, the pipe network was then solved using an iterative technique specially developed to solve hydraulic problems, i.e. the Hardy-Cross method [START_REF] Jm Martinez-Benet | A powerful improvement on the methodology for solving largescale pipeline networks[END_REF][START_REF] Djuric | Numerically oriented improved Hardy-Cross method[END_REF]. This specific method makes it possible to determine the airflow rates in each network duct as defined by the room walls and product surfaces from the mass flow rate at the boundary conditions. However, as the Hardy-Cross method neglected fluid momentum and considered that pressure gradients were the basic driving forces within the network, a customization of pressure drop coefficients was set up in order to avoid the solving of additional partial differential momentum equations which would have compromised both the computational simplicity and the rapidity of the model. Indeed, as it was well known that in some areas of a modern ripening chamber -above all the inlet and downwards areas and level with the room floor and the extraction region -fluid momentum took precedence over pressure gradients, this phenomenon had to be taken into account when modelling the evolution of the airflows. The customization of pressure drop coefficients amounted to introducing factors to artificially increase or decrease certain head drop coefficients to force the airflows to follow preferential paths inside the pipe network.

The first step in using the fluid dynamics model consists in defining the degree of precision required and assessing both the main geometrical and fluid dynamic characteristics of each duct in the pipe network as a function of the room's geometrical characteristics and of the type, number and relative location of the products. Pressure drop coefficients are then calculated from the classical rules of hydraulics and calibrated by means of corrective factors determined from relations established on the basis of general information obtained from experimental data processing. For each mesh of the pipe network, the model checks whether the energy balance equation is satisfied with a degree of precision lower than that actually required, and if necessary adds a corrective mass flow rate. The process is iterated throughout the entire pipe network until the energy balance equation is satisfied for every mesh with the required degree of precision. When considering a network configuration corresponding to a single rack filled with 18 salamis (3 rows per 6 columns) with degree of precision set to 50 Pa, Rizzi [START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF] indicated that the resulting network made of 90 nodes and 72 cells was solved in about 600 iterations, with an average computation time of about 5 seconds when using a Pentium II 400 MHz processor.

The fluid dynamics model satisfactorily predicted air velocity distribution as a function of overall mass flow rate entering the drying room and, above all, as a function of steady-state sharing of the airflow rate between the plant's two blower ducts [START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF].

Together, these numerical studies [START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF][START_REF] Ps Mirade | Etude numérique en 2 dimensions du cycle de ventilation d'un séchoir à saucisson moderne[END_REF][START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF] have provided useful information on air circulation during the ventilation cycle, but have not accurately analysed the dynamic operation of the meat dryers since only steady-state numerical models were built.

C. Unsteady Numerical Investigation

The ability of CFD to dynamically predict airflow patterns inside in a modern sausage dryer by means of 2D numerical models using time-dependent boundary conditions (i.e. an unsteady model) to accurately reproduce real operating conditions was recently assessed [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. Mirade [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF] studied the effect on ventilation homogeneity of modifying amplitude (four levels tested: 80%/20%, 70%/30%, 65%/35% and 60%/40%) and form (linear [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF] or sinusoidal [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]) during one period of the ventilation cycle. In the case of a sinusoidal form, Mirade [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF] also numerically evaluated the change in airflow structure due to dissymmetry of 2%, 5% or 10% of the ventilation cycle due to a dysfunction of the plant, which could occur in industry due to the simplicity of the system regulating airflow rate distribution between the two blower ducts and the marked unsteadiness of the airflow around a 50%/50% distribution.

The layout of the small industrial sausage dryer used in the studies of Mirade [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF] for building the dynamic CFD model was absolutely identical to that of Figure 1, with a height of 2.96 m and a width of 2.45 m. In this plant, the air was blown in through two stainless steel ducts placed on each side that were fitted with eight plastic conical jets 0.195 m long and 0.063 m in diameter. The air was extracted at the top through two other stainless steel ducts set 0.50 m apart and fitted with ten plastic extraction apertures of 0.08 m in diameter. The height of the free space from the ends of the conical jets to the floor was 2.32 m and the air velocity at the output of the jets was 5 m.s -1 when the ventilation corresponded to a 50%/50% configuration. The filling of the dryer in the numerical models was represented using 24 sausages of rectangular cross-section (0.50 m x 0.05 m), with eight sausages set 0.15 m apart at each of the three heights. The distance between two consecutive heights was 0.3 m, and the distance between the first rack of sausages and the floor was 0.35 m.

Features of Unsteady Modelling

Starting with the geometrical configuration presented in Figure 1, the CFD code Fluent v.5.1.1 and 5.4.8. [START_REF]Anonymous. Fluent 6: User's Guide[END_REF] was used to build a numerical model based on an unstructured 2D mesh of 25,500 tetrahedral cells. From the previous mesh, several variants of the 2D numerical model were constructed that corresponded to different forms and amplitudes of the ventilation cycle [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. Given that 2D modelling was used, the results had to be viewed with caution, not due to the 2D representation of a presumably 3D airflow blown by the conical jets, but rather due to the representation of the objects filling the device. Indeed, in 2D calculations, objects can act as a barrier, since the airflow cannot skirt around them as it does in reality, which almost certainly contributes to an increase in the heterogeneity of the airflow patterns. On the other hand, despite being performed in 2D, an unsteady CFD model has be particularly useful for assessing the dynamic operation of modern meat dryers.

To account for time-dependent boundary conditions due to the ventilation cycle, specific user-defined functions (UDF) were written in C++ programming language and applied to the inlet areas of the CFD models. In all calculations [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF], airflow was considered as incompressible, isothermal and -unlike the previous studies [START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF][START_REF] Ps Mirade | Etude numérique en 2 dimensions du cycle de ventilation d'un séchoir à saucisson moderne[END_REF][START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF] -unsteady. From preliminary tests, the time step increment was evaluated at 0.02 s so that the convergence of the calculations obtained for residuals lower than 10 -3 needed no more than 25-30 iterations at each time step [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF]. A total 3,000 time steps was therefore required to fully simulate just one period of the ventilation cycle that lasted 60 s.

More complex and costly -in terms of computation time -modelling procedures were used than in the previous studies [START_REF] Braconnier | Etude des écoulements d'air dans une étuve de séchage de charcuterie[END_REF][START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF][START_REF] Ps Mirade | Etude numérique en 2 dimensions du cycle de ventilation d'un séchoir à saucisson moderne[END_REF][START_REF] Rizzi | Development of a numerical model for the fluid dynamic simulation of an ascending flow ripening chamber[END_REF]. Indeed, main flow turbulence was taken into account by means of the Reynolds-stress model [START_REF] Zua Warsi | Fluid Dynamics: Theoretical and Computational Approaches[END_REF] -which needed the resolution of 6 equations instead of two for the k-ε model [START_REF] Be Launder | Mathematical Models of Turbulence[END_REF] -far from walls and objects, where a 'non-equilibrium' wall function was applied.

Moreover, a second upwind-differencing scheme [START_REF] Hirsch | Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows[END_REF] and the PISO algorithm [START_REF] Issa | Solution of the implicitly discretized fluid flow equations by operator-splitting[END_REF], instead of the SIMPLE algorithm, were also necessary in order to obtain accurate results.

Calculations were performed either on a 266 MHz Pentium II PC with 384 Mo of RAM or on a 2.2 GHz Pentium IV PC with 1.5 Go of RAM. Calculation time ranged from 55.2 to 59.6 hours on the Pentium II PC and from 8.3 to 9 hours on the Pentium IV PC, depending on the variant of the numerical model being solved.

Given that unsteady modelling was used, an initialisation of the calculations, i.e. the air velocity patterns at time zero, was required; this was obtained from a preliminary calculation where the inlet boundary conditions were steady and equal to 50% of the overall airflow rate in each of the two blower ducts. However, as this preliminary calculation needed unsteady modelling to reach convergence owing to the strong unsteadiness of the airflow in a 50%/50% configuration, it generated many air velocity patterns, thus forcing the author to check that the mean airflow structure determined over the full period of the ventilation cycle was not sensitive to initial conditions [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. To do this, Mirade [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF] performed three different simulations corresponding to different initial conditions and noted that the three mean airflow patterns obtained on the full period were the same.

Influence of the Amplitude of the Ventilation Cycle

Regardless of the form of the ventilation cycle, i.e. whether linear or sinusoidal, the influence of the ventilation cycle on airflow patterns can be summed up as follows [START_REF] Ps Mirade | Assessment of ventilation homogeneity in a modern sausage dryer by a dynamic CFD approach[END_REF][START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]: (i) air velocity distribution truly varies with the amplitude of the ventilation cycle; consequently, modern meat dryer has an optimum amplitude depending on its geometry (dimensions and location of the blower and extraction ducts) and filling level; (ii) above this optimal amplitude, there appears a marked heterogeneity in the ventilation, mainly according to the height between the lower part that is poorly ventilated and the upper part of the plant; and (iii) below the optimal amplitude, the heterogeneity also exits, but more according to the width of the plant, with high velocities concentrated towards the centre.

Figures 6a-d give the distribution of the air velocity means calculated on a vertical section of the dryer for a ventilation cycle of linear form, thus illustrating the influence of the amplitude of the ventilation cycle on airflow patterns [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. Before analysing Figures 6a-d, it should be noted that the symmetrical air velocity distribution in relation to the median plane of the plant proves that the unsteady CFD models correctly took into account the dynamic operation of the dryer induced by the ventilation cycle. 6a-d shows large differences in the distribution of air velocity means according to the linear ventilation cycle studied, with the best homogeneity corresponding to an amplitude of 65%/35% (Figure 6c), even though air velocity means ranged from 0.6 to slightly higher than 1.2 m.s -1 in the area filled with objects and despite the fact that a significant stratification of air velocities with height appeared in the plant, with air velocities higher than 1.2 m.s -1 for widths ranging from 975 to 1475 mm and for heights ranging from 1050 to 2250 mm [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF]. These findings are consistent with numerous industrial observations indicating that, in this type of dryer, the driest meat products are very often located in the upper part.

Comparison of Figures

Over and above this amplitude considered as an effective value to even out the air velocity distribution in the dryer, numerical results accounted for a marked heterogeneous distribution of air velocities with means ranging from 0.3 to more than 1.2 m.s -1 , as well as poorly ventilated areas in the lower part of the plant and at half-height at the left and right of the area filled with the objects, together with a highly-ventilated upper part of the dryer, with air velocity means peaking at 1.5 m.s -1 locally. Below the amplitude of 65%/35% (Figure 6d), air velocity means higher than 0.9 m.s -1 appeared in the lower part of the dryer compared with the three other cases (Figures 6a-c), thus giving rise to heterogeneity in ventilation according to the width of the dryer, with an area in the middle that was more ventilated than on either side.

Influence of the Form of the Ventilation Cycle

Unlike the cycle of linear form, with a sinusoidal form of the ventilation cycle that is certainly closer to industrial reality, a large poorly ventilated area with means lower than 0.6 m.s -1 appears in the lower part of the plant (Figure 7a) at an amplitude of 65%/35%, i.e. the value identified as the best amplitude for evening out the drying conditions in the case of a linear ventilation cycle. The airflow structure given by Figure 7a resembles that of a linear ventilation cycle of 70%/30% (Figure 6b). In view of the marked heterogeneity in the distribution of the airflow, an amplitude of 65%/35% was not optimal for a sinusoidal ventilation cycle [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF], meaning that, in addition to amplitude, the form of the ventilation cycle also has an influence on airflow patterns inside modern meat dryers.

Scaling down the amplitude of the ventilation cycle from 65%/35% to 60%/40% (Figure 7b) made the airflow patterns more homogeneous, as the poorly ventilated area in the lower part of the plant disappeared, leading to an airflow structure identical to the best one obtained for a linear ventilation cycle (Figure 6c).

The best results in terms of ventilation homogeneity were obtained for an amplitude of 65%/35% with a ventilation cycle of linear form, and for an amplitude of 60%/40% with ventilation cycle of sinusoidal form. This difference due to the form of the ventilation cycle can be explained from the findings of a previous 2D CFD study [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF]. Indeed, in an empty sausage dryer of similar geometry, Mirade and Daudin [START_REF] Ps Mirade | A numerical study of the airflow patterns in a sausage dryer[END_REF] demonstrated that for steady-state conditions of ventilation, (i) slight variations of +/-4% around 50%/50% in the low and high levels of the ventilation cycle provided adequate ventilation of the whole width of the dryer where the products are usually placed, and (ii) a strong imbalance between the airflow rates of the two blower ducts caused poor ventilation around the sausages. As the sinusoidal form leads rapidly to stronger imbalances than the linear form, the same ventilation homogeneity thus logically occurred with a ventilation cycle of lower amplitude [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF].

P.S. Mirade

Consequences of Dissymmetry in the Ventilation Cycle

As mentioned earlier, dysfunction in the ventilation cycle frequently occurs in industry as a result of the simplicity of the system distributing the airflow between the two blower ducts, and due to the marked unsteadiness of the airflow around the 50%/50% blower conditions.

Figures 8a-c show the unsteady numerical model results achieved for a sinusoidal ventilation cycle of amplitude 60%/40%, when a dissymmetry of 2% (Figure 8a), 5% (Figure 8b) or 10% (Figure 8c) is taken into account. The air velocity means were calculated over five full ventilation cycles, i.e. for a length of time (5 minutes) that is truly representative of what occurs in a real industrial setting when the ventilation is activated [START_REF] Ps Mirade | Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models[END_REF].

Figures 8a-c can be compared with Figure 7b to evaluate the change in airflow patterns due to dissymmetry. According to Figure 8a, a dissymmetry of 2% did not really affect the airflow distribution since the results were quite similar to those of the numerical model with no dissymmetry.

The higher air velocities were still concentrated at half-width and half-height in the modern sausage dryer. The only significant difference was an increase in air velocity means in the lower part of the dryer, for widths ranging from 1175 to 1275 mm and heights ranging from 450 to 850 mm.

Increasing the dissymmetry of the ventilation cycle from 2% to 5% clearly affected airflow patterns, leading to the appearance of dissymmetry between the two sides of the plant together with poorly ventilated areas with means lower than 0.6 m.s -1 in the lower part on each side (Figure 8b). The stratification of air velocity means according to height in the dryer also increased, almost certainly contributing to heterogeneity in product drying not only between top and bottom but also between the left and the right of the dryer. Predictably, a further increase in the dissymmetry of the ventilation cycle strongly disrupted means distribution for air velocity (Figure 8c). In the area filled with objects, air velocity means ranged from 0.3 m.s -1 in the lower part, where they formed a large area, to over 1.2 m.s -1 in the upper part.

According to Figures 8a-c, beyond 2% dissymmetry in the high and low levels of the ventilation cycle, it is essential to carefully regulate the ventilation cycle in order to prevent unwanted changes in airflow patterns that will almost certainly impair meat product drying.

IV MODERN MEAT DRYERS OF LARGE HEIGHT

A. Problematic

In the race to increase the competitiveness of dried meat products, production has been mechanized excessively in recent years with the introduction of robots to automatically move the trolleys filled with products from the manufacturing area to the drying area, and then, when dried, from the drying area to the packaging area. Consequently, modern meat dryers have become higher, reaching and sometimes exceeding 6 m, thus allowing the manufacture of the same quantity of dried meat products with a lower floor surface. Many manufacturers have reported poor meat drying in this type of dryer, particularly in the upper half just above the lateral blower ducts, where sausages appear too moist and too moulded during the drying process, thus revealing insufficiently ventilated areas. To cope with this problem, some plant designers have installed a specific system in order to invert airflows during the ventilation periods. Some systems blow air with a steady airflow rate without ventilation cycle via the ducts placed level with the ceiling and extract it via ducts fixed to the lateral walls of the plant. All the difficulty lies in adjusting the duration of the periods where the airflow is inverted in relation to the periods where the air is introduced through the lateral blower ducts according to the ventilation cycle.

Chanteloup [START_REF] Chanteloup | Implémentation de la notion d'âge moyen de l'air à l'aide d'une "User-Defined Function" dans le code Fluent[END_REF] recently studied the airflow patterns in two modern 6 m-high industrial sausage dryers based on unsteady 2D CFD modelling performed with the CFD code Fluent [START_REF]Anonymous. Fluent 6: User's Guide[END_REF], highlighting heterogeneity in airflow patterns in the case of standard dryer configurations. With the aim of evening out the airflow distribution, the author then tested the effects of modifying the amplitude and duration of the ventilation cycle, changing the height of the blower ducts, adding deflectors to force the air to penetrate inside the area filled with the sausages, adding a third extraction duct level with the ceiling, and inverting the airflow inlet.

B. Mean Age of Air

To investigate the effect of the previous modifications on the airflow patterns, the notion of Mean Age of Air (MAA) was introduced into the CFD models. MAA, which is widely used in building or cleanroom ventilation sciences, can be defined as the average lifetime of air at a particular location, giving an indication on the "freshness" of the air. In the framework of a ventilated room with a single inlet and a single outlet, local MAA corresponds to the average time it takes for air to travel from the inlet to any point inside the room [START_REF] Fisk | Air change effectiveness and pollutant removal efficiency during adverse mixing conditions[END_REF][START_REF] Federspiel | Air-change effectiveness: theory and calculation methods[END_REF][START_REF] Abanto | Airflow modelling in a computer room[END_REF][START_REF] Lin | Comparison of performances of displacement and mixing ventilations. Part II: indoor air quality[END_REF][START_REF] Rouaud | Numerical investigation on the efficiency of transient contaminant removal from a food processing clean room using ventilation effectiveness concepts[END_REF]. Moreover, MAA can be solved by CFD codes as an additional userdefined transported scalar following the equation corresponding to steady-state configurations:

τ τ τ τ ρ S x u x i i i = ∂ ∂ Γ - ∂ ∂ ) ( (1)
where τ is the MAA scalar, ρu i is the mass flow rate (ρ is the air density and u i is the air velocity), Γ is the diffusion coefficient of τ for the air mixture, and S τ is the source term of τ which depends on the density of the air mixture.

Several authors have reported that the diffusion coefficient and the source term of τ could be written following the two equations [START_REF] Fisk | Air change effectiveness and pollutant removal efficiency during adverse mixing conditions[END_REF][START_REF] Federspiel | Air-change effectiveness: theory and calculation methods[END_REF][START_REF] Abanto | Airflow modelling in a computer room[END_REF][START_REF] Lin | Comparison of performances of displacement and mixing ventilations. Part II: indoor air quality[END_REF][START_REF] Rouaud | Numerical investigation on the efficiency of transient contaminant removal from a food processing clean room using ventilation effectiveness concepts[END_REF][START_REF] Gan | Effective depth of fresh air distribution in rooms with single-sided natural ventilation[END_REF]:

7 . 0 10 88 . 2 5 EFF µ ρ τ + = Γ - (2) 1 = τ S ( 3
)
where µ EFF is the effective viscosity, which is related to both molecular viscosity and turbulent viscosity.

The boundary conditions for the solution of Eq. ( 1) are zero value at the air inlet and zero gradient at the air outlet and wall surfaces. Furthermore, age of air is a passive quantity which does not affect airflow patterns; hence, the local MAA is obtained from the solution of the airflow equation [START_REF] Gan | Effective depth of fresh air distribution in rooms with single-sided natural ventilation[END_REF].

By solving this scalar transport equation by means of a user-defined function incorporated into the Fluent code, Chanteloup [START_REF] Chanteloup | Implémentation de la notion d'âge moyen de l'air à l'aide d'une "User-Defined Function" dans le code Fluent[END_REF] calculated MAA distribution in different configurations of two modern sausage dryers of large heights with the aim of identifying a technical solution that evens out at best ventilation. In the standard dryer configuration, i.e. for one period of the ventilation cycle (amplitude of 90%/10%) and without air inlet inversion, the calculations indicated a lack of ventilation in the upper half of the plants compared with the lower half, with air velocities locally lower than 0.1 m.s -1 and an MAA peaking at 80 s at the level of the two rows immediately located just above the lateral blower ducts. Air velocities in the lower half of the dryer were higher, ranging from 0.3 to 0.6 m.s -1 , and the MAA values were lower, ranging from 58 to 70 s. These findings undoubtedly corroborate the observations made in industry, i.e. the appearance of over-moist and excessively moulded sausages just above the lateral blower ducts during the drying process in modern sausage dryers of large height.

Figure 9 displays the local MAA calculated in a 4.3 m-wide sausage dryer, taking into account an air inlet inversion of 2 min (Figure 9a), 3 min (Figure 9b), 4 min (Figure 9c) or 5 min (Figure 9d) during 10 minutes of ventilation [START_REF] Chanteloup | Implémentation de la notion d'âge moyen de l'air à l'aide d'une "User-Defined Function" dans le code Fluent[END_REF]. Even though numerical results revealed few differences in the air velocity distribution between the four configurations (air velocity means ranged from 0.17 to 0.24 m.s -1 in the area filled with the sausages), analysis of Figure 9 shows marked differences in local MAA distribution. Increasing the inversion of the air inlet led to marked gradients in MAA distribution in relation to height; when the inversion reached 5 min (Figure 9d), local MAA values ranged from less than 55 s level with the ceiling near the extraction ducts to over 105 s (exactly 130 s) in the lower part of the dryer (giving a mean of 79 s with a standard deviation of 27 s), whereas the heterogeneity of MAA distribution was much lower when using an inversion time of 2 min (Figure 9a), i.e. a mean of 67 s and a standard deviation of below 5 s between the top and bottom of the dryer. In light of these results, local MAA seems to be a better and a more sensitive parameter than air velocity for highlighting pockets of inadequate ventilation and thus for assessing ventilation efficiency in industrial food plants.

From the analysis of the local air velocity in combination with the local MAA distribution, Chanteloup [START_REF] Chanteloup | Implémentation de la notion d'âge moyen de l'air à l'aide d'une "User-Defined Function" dans le code Fluent[END_REF] numerically demonstrated that changing the height of the lateral blower ducts between 2 m to Finally, the numerical investigation carried out revealed that the best distribution of local MAA (mean value of 18 s and standard deviation below 1 s) was obtained when a 0.35 m-long horizontal deflector was fitted just above each lateral blower duct in the 5.3 m-wide modern sausage dryer, for an air inlet inverted for 2 min for every 10 min of ventilation (Figure 10). On the other hand, the air velocities were not homogeneously distributed around the sausages, since standard deviation reached 0.17 m.s -1 for a mean of 0.37 m.s -1 . In addition, the strong impact on the homogeneity of MAA distribution was much lower when the same deflectors were added in the numerical model corresponding to the second sausage dryer which was less wide. Taken together, these numerical conclusions confirm that airflow patterns are very difficult to assess a priori; they also underline that numerical results absolutely must be validated by experimental results.

V. CONCLUSION

This chapter clearly shows that CFD techniques can be very useful tools for assessing and improving airflow patterns in modern industrial meat dryers of medium or large height, particularly those operating due to the ventilation cycle. The effect of the amplitude and form of the ventilation cycle on the homogeneity of the distribution of the air velocity means has been illustrated, together with the effect of a dissymmetry in the ventilation cycle. The results obtained confirmed the industrial observations on poor process efficiency in some parts of the plants, such as, for example, that the driest products are often located in the upper part of medium-height meat dryers. The need for controlled regulation of the ventilation cycle was also highlighted. Calculations performed in modern sausage dryers of large height proved that local mean age of air (MAA) distribution was a highly promising and very useful parameter for assessing ventilation efficiency compared with the usual air velocity, even if numerical results needed to be validated by experimental data.

With CFD techniques, the significance and effects of operating conditions and design parameters can therefore be analysed to gain a better understanding of the dynamics of the meat drying. Furthermore, more recent studies assessing airflow patterns via unsteady modelling will shortly provide professionals with a rational approach to help them in the operation and design of modern dryers, once they will have been validated by experimental data However, a full numerical model of how a modern meat dryer operates would be ideal, i.e. a model describing the homogeneity of the drying conditions and the interaction between the meat products being dried and the indoor atmosphere (velocity, turbulence, temperature and relative humidity). This remains difficult because very refined meshes will need to be constructed, yielding 3D numerical models requiring immense memory size. However, further progress can be expected in the years to come as the CFD codes become more and more flexible in use while the calculating power of computers currently used in practice continues to increase.

Area of filling with sausages

4. 1 m

 1 had a very poor effect in evening out the ventilation in the area filled with the sausages, whatever the width of the dryer: 4.3 m or 5.3 m. The air velocity means ranged from 0.38 to 0.44 m.s -1 (with a standard deviation of 0.19/0.20 m.s -1 ), and MAA means ranged from 33 to 35 s with a standard deviation below 5 s in all cases. Halving the duration of the ventilation cycle from 60 s to 30 s combined with the addition of a third extraction duct level with the ceiling slightly affected airflow patterns inside the large-height dryers studied. As indicated in Figure9, inverting the air inlet in the dryer significantly modified air distribution in the plant, even improving ventilation homogeneity around the sausages compared with a standard operation without air inlet inversion, provided that the inversion time did not exceed one fifth of the total ventilation time. On the other hand, scaling down the amplitude of the ventilation cycle from 90%/10% to 60%/40% without inverting the air inlet during ventilation logically led to an increase in air velocities around the sausages located in the lower half of the plant to the detriment of the upper half, thus increasing the height stratification phenomenon, particularly in terms of local MAA distribution.

Figure 1 .

 1 Figure 1. Layout of a typical modern meat dryer according to a vertical section with a schematic

Figure 2 .

 2 Figure 2. Description of the airflow rate evolution between each of the two blower ducts during one

Figure 3 .

 3 Figure 3. Evolution in air relative humidity during the operation of a modern meat dryer according to

Figure 4 .

 4 Figure 4. Distribution of the air velocities calculated from 3D CFD modelling on a vertical section located at half-length of a 134 m 3 small-scale sausage dryer corresponding to three steady-state

Figure 5 .

 5 Figure 5. Distribution of the air velocity means calculated from 2D CFD modelling on a vertical section of a 134 m 3 small-scale sausage dryer for a ventilation cycle of linear form at amplitude

Figure 6 .

 6 Figure 6. Distribution of the air velocity means calculated from 2D unsteady CFD modelling on a

Figure 7 .

 7 Figure 7. Distribution of the air velocity means calculated from 2D unsteady CFD modelling on a

Figure 8 .

 8 Figure 8. Distribution of the air velocity means calculated from 2D unsteady CFD modelling on a

Figure 9 .

 9 Figure 9. Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD

Figure 10 .

 10 Figure 10. Distribution of the local mean age of air (MAA) calculated from 2D unsteady CFD

  Figure 1