E Goncalves
email: eric.goncalves@legi.grenoble-inp.fr

R Houdeville

Numerical simulations of a transport-aircraft configuration

Keywords: CFD, aerodynamics, turbulence models, 3D separation, vortical structures

An implicit low-cost Navier-Stokes solver combined with a multigrid algorithm and wall functions has been developed for efficient numerical simulations on a realistic wing-body aircraft configuration. A study of the behavior of different transport-equation turbulence models is given. Comparisons are made with experimental data. The structure of the three-dimensional flow separation predicted by computations is described and its topological coherence is checked.

INTRODUCTION

During the last decade, considerable progress has been made in the development and validation of numerical simulation solvers for complex aerodynamic applications. Today, advanced numerical tools are intensively used in the design process of aerospace components which involve three-dimensional turbulent flows with separation. However, CFD codes still suffer from deficiencies in representability of computations with respect to the physics, from the lack of accuracy and robustness and from large CPU costs. Indeed, despite the computers growing capacity, the resolution of the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with a transport-equation turbulence model, integrated down to the wall, for a complete aircraft configuration remains expensive.

In order to reduce the CPU cost, different strategies have been explored : implicit methods, multigrid algorithm and parallel computing. Another possibility to avoid the full Navier-Stokes resolution is the use of wall functions as boundary conditions. Thanks to the robustness improvement, the quality of results in two-dimensional separated flows and the CPU cost saving, the wall law approach is a promising method [START_REF] Mohammadi | Unsteady separated turbulent flows computation with walllaws and kε model[END_REF][START_REF] Craft | A new wall function strategy for complex turbulent flows[END_REF][START_REF] Kalitzin | Near-wall behavior of RANS turbulence models and implications for wall functions[END_REF]. However, the existence of a law of the wall for three-dimensional flows is still an open issue. Olcmen [START_REF] Olcmen | Perspective : on the near wall similarity of threedimensional turbulent boundary layers[END_REF] has investigated the possible existence of a universal velocity profile in three-dimensional boundary layers and has concluded that there is not strong evidence for such a 3D turbulent boundary layer velocity profile, neither for the streamwise component nor for the transversal component. In the numerical study of the flow around an ellipsoid, Tsai and Withney [START_REF] Tsai | Numerical study of three-dimensional flow separation for a 6:1 ellipsoid[END_REF]) used a logarithmic law for the streamwise direction but changed the value of the constant to obtain a good agreement with the experimental data.

In the present study, we propose a low-cost implicit solver coupled with a multigrid algorithm and the use of a wall law approach to investigate the 3D flow around a wing-body configuration. Moreover, the behavior of four popular turbulence models is compared. This configuration has been a European test-case to validate CFD codes and turbulence modeling. It was computed by LeBalleur (LeBalleur et al. 1997) using a defect-formulation theory and a 3D thin-layer approach. RANS computations have been performed with the Baldwin-Lomax model [START_REF] Elsholtz | 3D Navier-Stokes mesh generation and analysis of viscous flow solution around the DLR-F4 wing-body configuration. ECARP -Validation of CFD Codes and Assessment of Turbulence Models[END_REF], the Granville algebraic model, the one-equation Wolsthein model and the Chen-Patel two-layer model [START_REF] Tourrette | Assessment of turbulence models for the transonic flow around the DLR-F4 wing/body configuration[END_REF]) and also with an improved kω model (Kroll et al. 2000). A study of a drag polar has been realized with the kω linearized algebraic stress (LEA) model [START_REF] Rakowitz | Structured and unstructured computations on the DLR-F4 wing-body configurations[END_REF]. Recently computations with explicit algebraic Reynoldsstress models (EARSM) have been performed and attention was drawn to the leading-edge separation pocket on the outboard part of the wing [START_REF] Franke | Assessment of explicit algebraic Reynolds-stress turbulence models in aerodynamic compuations[END_REF]. Regarding the shock location, algebraic models can not give predictions with an acceptable level of accuracy. At least a transport-equation model, which takes into consideration history effects, is required to accurately model 3D flow phenomena.

Finally, a study of the wing-fuselage junction flow is proposed. The adverse pressure gradient in the streamwise direction imposed by the wing often causes the upwind boundary layer on the body to separate and to form a horseshoe vortex around the wing. On the trailing edge, the horseshoe vortex feeds a vortical structure, called tornado vortex. The topological coherence of numerical vortices is checked based on the critical-point theory.

GOVERNING EQUATIONS AND TURBULENCE MODELS

Reynolds-Averaged Navier-Stokes equations

The compressible RANS equations coupled with a two-equation turbulence model can be expressed as :

∂w ∂t + div (F c -F v ) = S (1) w =       ρ ρV ρE ρk ρΨ       ; F c =       ρV ρV ⊗ V + pI (ρE + p)V ρkV ρΨV       ; F v =        0 τ v + τ t (τ v + τ t ).V -q v -q t (µ + µ t /σ k ) grad k (µ + µ t /σ Ψ ) grad Ψ       
where w denotes the conservative variables, F c and F v the convective and viscous flux densities and S the source terms which concern only the transport equations. Ψ is the length scale determining variable.

The exact expression of the eddy viscosity µ t and the source terms depends on the turbulence model, as well as the constants σ k and σ Ψ . The total stress tensor τ is evaluated following the Stokes hypothesis and the Boussinesq assumption. The total heat flux vector q is obtained from the Fourier law with the constant Prandtl number hypothesis.

τ = τ v + τ t = (µ + µ t ) 1 2 ( grad V + ( grad V ) t ) - 2 3 ( div V )I + 2 3 kI (2) q = q v + q t = - µ P r + µ t P rt C p grad T (3)
The viscosity is determined by the Sutherland law.

Turbulence Models and Wall law approach

Various two-equation turbulence models are used in the present study : the Smith kl model [START_REF] Smith | A Near Wall Model for the kl Two Equation Turbulence Model[END_REF], the Wilcox kω model (Wilcox 1988), the Menter SST kω model [START_REF] Menter | Zonal two equation kω turbulence models for aerodynamic flows[END_REF][START_REF] Menter | Two-equation eddy-viscosity turbulence models for engineering applications[END_REF]) and also the one-equation Spalart-Allmaras [START_REF] Spalart | A one-equation turbulence model for aerodynamic flows[END_REF].

At the wall, a no-slip condition is used coupled to a wall law treatment. It consists in imposing the diffusive flux densities, required for the integration process, in adjacent cells to a wall. The shear stress τ and the heat flux q are obtained from an analytical velocity profile

u + = y + if y + < 11.13 u + = 1 κ ln y + + 5.25 if y + > 11.13 u + = u/U τ ; y + = yU τ ν w (4)
and from the integration of the total enthalpy equation, in which the convection is neglected

uτ xy -q y = -q w (5)
where x and y denote here the longitudinal and normal direction with respect to the wall.

In equation (4), u represents the van Driest (1951,1957) transformed velocity for compressible flows

u = u 0 ρ ρ w du (6)
For an adiabatic wall, integration of equations ( 5) and ( 6) gives

T w -T = A u 2 2 ; A = µ + µ t C p µ P r + µ t P rt (7) u = 1 √ B arcsin( √ Bu) ; B = A 2T w (8)
The wall law treatment is now straightforward. Knowing u from the Navier-Stokes solution, relationships (7) and (8) give u. The shear stress value is obtained from (4) and is assumed constant in the wall normal direction. To compute boundary layer separation, the wall law is expressed in a reference frame defined by the velocity direction in adjacent cells to a wall. Such a treatment is not in contradiction with the fact that the log law does not exist in separated regions. Actually, in these regions, τ w remains small and therefore y + is small, leading to the use of the linear part of the velocity profile. This is equivalent to computing the velocity gradient over two points instead of three for the ordinary cells.

For three-dimensional boundary layers, the existence of a wall law is assumed valid for the streamwise velocity component. Moreover, in adjacent cells to a wall, the velocity is supposed colinear to the wall friction direction. This is the only assumption made regarding the transversal velocity component.

As concerns the transport equations of the turbulence models, k is set to 0 at the wall and its production is imposed according to the formulation proposed by Viegas and Rubesin (Viegas andRubesin 1983, 1985) where the thickness of the viscous sub-layer y + v is assumed constant

(P k ) 1 = τ 3/2 w 2κy 1 √ ρ w ln 2y 1 y v (9)
For the two-equation models, the second variable is deduced from an analytical relation and is imposed in adjacent cells to a wall. The characteristic length scale of the Chen model (Chen and Patel 1988) is used for the specific dissipation ω and a classical linear law for the length l.

For the one-equation Spalart-Allmaras model, the transported quantity is imposed in adjacent cells to a wall by using the closure relations of the model, the velocity profile and a mixing-length formulation for the eddy viscosity. More details concerning the wall law approach are given in reference [START_REF] Goncalves | Reassessment of the wall functions approach for RANS computations[END_REF].

NUMERICAL METHODS

The numerical simulations were carried out using an implicit CFD code solving the uncoupled RANS/turbulent systems for multi-domain structured meshes. This solver is based on a cellcentered finite-volume discretization.

Spatial discretization

The system in integral form is written for a computational cell of volume Ω limited by a surface Σ and with an outer normal n. These equations can be expressed as :

d dt Ω w dΩ + Σ F c .n dΣ - Σ F v .n dΣ = Ω S dΩ (10)
Using the finite-volume technique for space discretization, a semi-discrete form of equations may be written as:

Ω ∂w ∂t + allf aces (F c -F v ).nΣ = ΩS (11)
For the mean flow, the convective flux density vector on a cell face is computed with the space-centered Jameson scheme stabilized by a scalar artificial dissipation [START_REF] Jameson | Numerical simulation of the Euler equations by finite volume method using Runge-Kutta time stepping schemes[END_REF]. The dissipative operator comprises second (parameter k 2 ) and fourth (parameter k 4 ) order differences.

Discretization of the viscous terms is performed by a second-order space-centered scheme.

For the turbulence transport equations, the upwind Roe scheme [START_REF] Roe | Approximate Riemann solvers, parameters vectors, and difference schemes[END_REF]) was used to obtain a more robust method. The second-order accuracy was obtained by introducing a flux-limited dissipation [START_REF] Tatsumi | Flux-Limited Schemes for the Compressible Navier-Stokes Equations[END_REF].

Temporal discretization

Time integration is achieved through a low-cost implicit method [START_REF] Luo | A fast, matrix-free implicit method for compressible flows on unstructured grids[END_REF][START_REF] Luo | An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids[END_REF]. The implicit method consists in solving a system of equations arising from the linearization of a fully implicit scheme, at each time step. The main feature of this method is that the storage of the Jacobian matrix is completely eliminated, which leads to a low-storage algorithm. The viscous flux Jacobian matrices are replaced by their spectral radii. The convective flux are written with the Roe scheme instead of the Jameson scheme because of the dissipation term, the use of an inconsistent linearization having no consequence for steady computations. The Jacobian matrices which appear from the linearization of the centered fluxes are approximated with the numerical fluxes. The following system is obtained, for the iteration n:

∆w n + l=i,j,k σ l δ l µ l (∆f n l ) -σ l δ l (ρ V l I d ∆w n ) -σ l δ l (D l δ l ∆w n ) = R n expl ( 12
)
where ∆w n = w n+1 -w n , σ l = ∆t/∆x l , and R n expl represents the explicit conservative residuals. For each direction l, ρ V l is the viscous spectral radius, µ l is the averaged operator, δ l is the difference operator, f l is the physical convective flux and D l the dissipation matrix. Then, the numerical dissipation matrices are replaced by their spectral radii and the system becomes matrix-free.

The implicit time-integration procedure leads to a system which can be solved directly or iteratively. The direct inversion can be memory intensive and computationally expensive. Therefore, an implicit relaxation procedure is preferred and the point Jacobi relaxation algorithm was chosen.

Concerning the turbulence transport equations, the diffusive flux Jacobian matrix is also replaced by its spectral radius. The source term needs a special treatment [START_REF] Merci | Computational treatment of source terms in two-equation turbulence models[END_REF]. Only the negative part of the source term Jacobian matrix is considered and replaced by its spectral radius. The system obtained is solved with a line-alternated Jacobi relaxation algorithm.

For steady state computations, convergence acceleration was obtained using a local time step and the full approximation storage (FAS) multigrid method proposed by Jameson [START_REF] Jameson | Multigrid Algoritms for Compressible Flow Calculations[END_REF]. Forcing functions are defined on the coarser grids and added to the residuals used for the stepping scheme. The corrections computed on each coarse grid are transferred back to the finer one by trilinear interpolations. The turbulent equations are only solved on the fine grid and the computed eddy viscosity µ t is transferred to the coarse grids. The multigrid algorithm is applied through a V -type cycle.

Wall boundary condition

At the wall, a no-slip condition was used coupled to a wall law treatment. It consists in imposing the diffusive flux densities, required for the integration process, in adjacent cells to a wall. The shear stress τ and the heat flux q are obtained from the analytical velocity profile (4).

When using the wall law approach with the multigrid algorithm, the wall law boundary condition is applied on the fine grid and the classical no-slip condition is applied on the coarse grids.

Turbulence Models

As the discretization scheme does not insure the positivity of the turbulent conservative variables, limiters are used to avoid negative k or ε values. These limiters are set equal to the corresponding imposed boundary values in the far field.

COMPARISON TO EXPERIMENTS

Experimental conditions

The DLR-F4 wing-body configuration has been studied experimentally in three different European wind tunnels [START_REF] Redeker | Experiments on the DLR-F4 wing-body configuration in several European windtunnels[END_REF]. The model is representative of a realistic transportaircraft configuration (1,17m span and 1.19m body length) with a high aspect ratio transonic wing and an Airbus-type fuselage. The test case is defined as follows : M ∞ = 0.75, Mach number α = 0.93 o , angle of attack T i = 300K, stagnation temperature Re c = 3 10 6 , Reynolds number based on the aerodynamic mean chord equal to 0.14m.

Mesh

The mesh used is a single block C -O which defines half of the wing-body configuration. It contains 1026715 nodes, 257 nodes in the main direction, 85 in the normal direction of the wing and 47 in the spanwise direction along the wing. The outer boundaries are fixed at approximatively 4 fuselage-lengths (FL) upstream, one FL below and above the configuration and 3 FL downstream. In the spanwise direction, the mesh covers one additional FL. A special contraction of the mesh is applied in the main flow direction, on the upper side of the wing, in the shock wave area. The goal of the paper is not to obtain the best results with the finest mesh, but to obtain a reasonable quality of results at low cost. Thus, neither a grid refinement study nor a study of the influence of far-field distance were undertaken. The y + values, at the center of the first cells, vary between 1 and 30 on the wing and between 30 and 80 on the fuselage. Views of the mesh on the solid walls are given in Figure 1.

Numerical parameters

Computations are started from an uniform flow-field using a local time step. The numerical parameters used are : -the CFL number, 10 -Jacobi iterations for the implicit stage, 14 -grids levels with multigrid algorithm, 2 -parameter k 2 of artificial dissipation: 0.5 -parameter k 4 of artificial dissipation: 0.032 for Jones-Launder and Wilcox models, 0.016 for other ones -the farfield value of turbulent viscosity µ t∞ = 0.1µ ∞ -the farfield value of turbulent kinetic energy k ∞ = 0.0012 m 2 /s 2 -the farfield value of dissipation rate ε ∞ = 42 m 2 /s 3 -the farfield value of specific dissipation ω ∞ = 3500 s -1 For the computations, the flow is assumed to be fully turbulent.

Convergence and CPU time

In Figure 2 is plotted the evolution of residuals for computations without multigrid algorithm and with two grids level. Both computations have been carried out with the kl model. The use of an implicit solver coupled with a multigrid strategy and wall functions allows to obtain a steady converged result with only 1000 iterations (about 55 minutes on a NEC-SX5 computer). For one-grid computations with two-equation models, the CPU time for 1000 iterations is about 2400s, except the SST model, which needs about 6% more time. Two-grid computations need about 45% more computational time. Faster computations could be obtained by using more efficient multigrid algorithm such as an adaptative-smoothing procedure [START_REF] Drikakis | Acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure[END_REF].

Aerodynamic coefficients

The values of the aerodynamic coefficients of the complete configuration are reported in table 1, for each turbulence model. The best lift coefficient is obtained with the Spalart-Allmaras model (only 1.5 % of error). The Wilcox model over-predicts the lift coefficient (around 11%) whereas the SST Menter model under-predicts it. For all computations, the drag coefficient is largely under-estimated, especially with the Menter model (around 25% of error).

Pressure coefficient

The pressure coefficient distribution is shown in Figure 3, for three spanwise sections on the wing. The pressure level near the leading edge, on the suction side, is underestimated by all computations. At the closest section to the body, y/b = 0.185, the best result is obtained with the kl model. The Spalart-Allmaras and Menter SST models predict a large and unrealistic separation at the trailing edge. This was also observed on DLR-F6 wing-body computations [START_REF] Schwamborn | DLR F6. In: Haase, Aupoix, Bunge and Schwamborn[END_REF]. At the other sections, the shock location is well predicted with the Spalart-Allmaras model and a little downstream with the Smith model. As observed for two-dimensional computations, the Wilcox model predicts a shock location far away from the experimental data and the SST Menter model at an upstream location.

Skin friction coefficient

The evolution of the skin friction coefficient in the streamwise direction, on the suction side, is presented in Figure 4. There are no experimental values available, only an oil flow picture which does not show any shock-induced separation, which is well predicted by all computations. The SST Menter model gives the lowest skin friction levels. Near the wing root, the Spalart-Allmaras model is close to the Menter model.

Deviation angle

The evolution of the deviation angle β 0 (angle between the wall friction and the velocity at the boundary layer edge), on the suction side, is considered in Figure 5. There is a clearly pronounced peak at the shock location, the wall flow being deviated towards the wing tip. The SST model predicts large values of the deviation in the shock region and at the trailing edge. At the closest section to the body, as noticed on the pressure distribution, the Spalart-Allmaras and Menter models predict a large separation.

Vortical structures

The skin friction lines over the half configuration are plotted in Figure 6, computed with the Smith model. A horseshoe vortex footprint around the wing root can be seen and also a vortical structure footprint at the trailing edge, near the root of the wing. The experimental oil flow picture also shows a vortex-like structure at the wing root but there is no flow visualization for the fuselage.

An enlargement of the wing/body junction, at the leading edge of the wing, is presented in Figure 7. We can well observe the horseshoe vortex around the root, the saddle point on the fuselage and the stagnation point on the wing. Such a separation has been evidenced by Furlano [START_REF] Furlano | Steady and unsteady computations of flows close to airfoil buffeting: validation of turbulence models[END_REF] for 3D computations of an airfoil between walls, using the kl Smith model. In these results, the stagnation point is located on the fuselage. In the present case, it is certainly the sweep angle effect which moves the stagnation point on the wing. It can be noted that all turbulence models predict the same flow topology.

The horseshoe vortex feeds a vortical structure, called tornado vortex. The footprint of this vortex on the wing and the body is a focus, interpreted as a rolling up of the separation surface. This structure is generated by the interaction between the boundary layers of the wing and the fuselage [START_REF] Delery | Physics of vortical flows[END_REF]. A detail of the wing/body junction, at the trailing edge of the wing, is presented in Figure 8, computed with the Smith model. The tornado vortex with the two foci are clearly evidenced. We note a third focus on the fuselage, interpreted as an unrolling up of the flow, which feeds the focus on the body, already fed by the horseshoe vortex. This third focus allows to preserve the volume of the stagnation flow of the vortical structure. Moreover, when using a very large close-up view of the trailing edge vicinity, it has been possible to identify a second saddle point and a node near the third focus, on the wing/body junction. Downstream of the tornado vortex, on the fuselage, is located a third saddle point which ends the horseshoe vortex surrounding the wing/body junction. Finally, we have three foci, three saddle points and two nodes (the stagnation point being equivalent to a node). To check the coherence of the three-dimensional separation, we use the following relation based on the critical-point theory and only valid for an isolated obstacle [START_REF] Delery | Physics of vortical flows[END_REF][START_REF] Delery | Robert Legendre and Henri Werle : toward the elucidation of threedimensional separation[END_REF]) : Σ(nodes and foci) -Σ(saddle points) = 2 (13)

This relation is well respected but one should be careful, the identification of all critical points could be difficult.

When compared to the result obtained with the Smith model, the vortical structure predicted by the Wilcox model (Figure 9) and the Spalart-Allmaras model (Figure 10) presents a similar topology. This structure is a little less extended for the first model and largely overestimated by the second one. The big vortical structure with five foci predicted by the SST Menter model (Figure 11) is completely unphysical. This is certainly due to the SST correction based on the Bradshaw hypothesis, established only for two-dimensional turbulent boundary layers. This is consistent with conclusions derived from other studies on 3D configurations [START_REF] Apsley | Investigation of advanced turbulence models for the flow in a generic wing-body junction[END_REF]Leschziner 2001, Leschziner 2006).

CONCLUSION

An efficient compressible CFD method has been presented and applied to a realistic aircraft configuration. The combination of a low-storage implicit method, the FAS multigrid algorithm and wall functions allows to largely reduce the CPU cost. Presented numerical results verify the ability of the numerical tool to correctly predict the three-dimensional flow. Four popular turbulence models have been tested and compared. Only indications of the models behavior can be provided considering the complexity of the flow and the experimental data available. When comparing the pressure coefficient distribution, the Smith and the Spalart-Allmaras models provide the best results. Yet, near the wing root, the Spalart-Allmaras model predicts a large and unrealistic separation. As observed for two-dimensional computations over airfoils, the Wilcox model predicts a shock location far away from the experimental data and the SST Menter model at an upstream location.

With regard to the 3D separated flow generated on the wing-body junction, all models predict a coherent topological structure, except the SST Menter model which yields an unphysical vortical structure. This is certainly due to the rigid link the SST limiter establishes between the turbulence energy and shear stress.

Fig1Fig7:

  Fig1: Views of the mesh

Figure 10 .

 10 Figure 1. Views of the mesh

  Even if global results are acceptable, the use of the SST correction for 3D flows should be clarified. Additional works are in progress to simulate unsteady three-dimensional flows, to develop low dissipative numerical schemes and to pursue comparative analyses between turbulence models.Wilcox, D.C., 1988. Reassessment of the scale-determining equation for advanced turbulence models. AIAA Journal, 26(11), 1299-1310.

	List of Figures

Table 1 .

 1 Lift and drag coefficients

		LIFT	error	DRAG	error
	experiment	0.602	-	0.0352	-
	k -l	0.638	6 %	0.0303	14 %
	k -ω	0.67	11 %	0.0306	13 %
	k -ω SST	0.571	5 %	0.0261	25 %
	Spalart-Allmaras	0.61	1.5 %	0.0283	19.5 %


Dan Xu

Classifiers and some typological considerations 1

Keywords: classifier, typology, word order, complementary distribution

Classifiers, both nominal and verbal, must be taken into consideration as a parameter in typological studies of the numeral classifier languages. Building on previous work, we will show that nominal and verbal classifiers are mutually dependent both chronologically and in terms of their syntactic position. Cross-linguistic data in general, and Chinese in particular, illustrate this dependency: nominal classifiers develop before verbal classifiers and the word order of the two kinds of classifiers is in a complementary distribution, occurring before nouns and after verbs.

Introduction

 Since Greenberg's (1963)works on language typology, discussions and studies of this topic have flourished in general linguistics, and the number of investigated languages has increased considerably. [START_REF] Dryer | The Greenbergian word order correlations[END_REF][START_REF] Dryer | Word Order in Sino-Tibetan Languages from a Typological and Geographical Perspective[END_REF] studies of numerous typological characteristics, for example, are based on 625 language samples. According to Dryer, the Chinese language (contemporary Mandarin) is considered an atypical VO language. Some Chinese scholars have also tried to test the assumptions established by Greenberg and Dryer. Among them, Liu Danqing (2003) has analyzed Chinese languages, while Huang [START_REF] Xing | Woguo shaoshu minzu yuyan de cixu leixing' (The Word Order typology of minority languages in China)[END_REF] has investigated non-Han languages in China. Their works confirm, for the most part, the ideas put forward by Greenberg (1966) and [START_REF] Dryer | The Greenbergian word order correlations[END_REF]. Numerous significant works have been published on different languages. The focus of previous research was predominantly on word order and its plausible implicational relationships with other features. The presence of classifiers in numeral classifier languages, however, was not a salient feature in these studies and their relevance for word order sometimes neglected. Only recent works by Haspelmath et al. (2005) and [START_REF] Comrie | The Areal Typology of Chinese: Between North and Southeast Asia[END_REF] began to take classifiers into account as one of the typological parameters in noun phrases. Indeed, in languages with obligatory numeral classifiers, they play an important role in word order typology, at least in Asian languages. Since a majority of these languages belonging to the Sino-Tibetan, Altaic, and Austro-Asiatic families, are in close contact in China, it is interesting to compare how classifiers function and how they influence word order in Chinese (contemporary and classical) and in non-Han languages of China. Our work will build on the significant research results found in Chinese publications, such as Sun [START_REF] Hongkai | Zangmianyu liangci yongfa bijiao' (Comparison of classifiers in Tibeto-Burman Languages)[END_REF], [START_REF] Qingxia | Mengya qi liangci de leixingxue tezheng-Jingpo yu liangci de ge'an yanjiu (Typological characteristics of classifiers at a primitive stage-the case of Jingpo), Studies on Sino-Tibetan languages: Papers in honor of Professor Hwang-Cherng Gong on his seventieth Birthday[END_REF], Li Jinfang and Hu Suhua (eds. 2005), and others.

In this paper, we use 'nominal classifiers' in its usual interpretation: morphemes that denote the shape or class of the referent and used in conjunction with 1 Our gratitude goes to Alain Peyraube who warmly received us when we first came to France in 1982 as graduate students. He has given us enormous support during our studies in Chinese linguistic research.

Our works have been supported by the grant Quantification et Pluralité ANR-06-BLAN0259 awarded by the Research Department of the French Government.

We thank the anonymous reviewer for his/her constructive comments and suggestions.

the numeral of an NP (Akhenvald, 2000:97). They are to be distinguished from 'measure words', which express measuring units of the referent of the noun. (Akhenvald, 2000:149) and is found in some American Indian languages and languages of New Guinea and Australia (Akhenvald, 2000:169-171). We define the term as words that measure the action expressed by the VP. For example, in Chinese, (3a) is contrasted with (3b) in the use of verbal classifier.

(3)a. 我听过两次他的讲演 wǒ tīng-guò liǎng-cì tā de jiǎngyǎn I listen-EXP two-time his POSS speech 'I have listened to his speech twice.' b. 我听过两遍他的讲演 wǒ tīng-guò liǎng-biàn tā de jiǎngyǎn I listen-EXP two-time his POSS speech 'I have listened to his whole speech twice.'

Both cì and biàn provides the unit for counting the number of times of the event. However biàn has the additional implication that the event takes place from the beginning to the end, in this case, the whole lecture twice. On the other hand the verbal classifier cì does not imply the whole process. It could well mean two times and each time for a short period. In this sense, not all languages have verbal classifiers, only few languages like Chinese do.

Nominal classifiers have been extensively examined and discussed, but verbal classifiers seem to be less studied. In this paper, we try to understand the syntactic distribution of nominal classifiers and verbal classifiers and their relationship. We believe that the order Numeral Noun (NumN) has to be studied together with classifiers (CL) in languages with obligatory NumCL. It appears that nominal CL generally develop before verbal CL and the distribution of nominal CL and verbal CL shows a mirror symmetric word order (see also [START_REF] Shi | Yufahua de dongyin yu jizhi (Motivation and Mechanism of Grammaticalization)[END_REF] and the same mirror word order will be shown to be true in cross linguistic data at hand. We will offer tentative explanations on why this is so at the end of this paper.

Numeral and noun

To examine the evolution of numeral classifier and verbal classifier, we will start with numeral classifier first and with the pre-numeral classifier stage, in which Num directly modifies Noun.

In the literature on typology (Dryer, 1992: 119), the pair NumN and NNum is left unclassified. NumN/NNum order clearly shows a correlation with VO/OV type except in languages of Africa. It is evident in Dryer's statistics that the order NumN strongly correlates with VO order cross-linguistically. Dryer states that "the two orders of numeral and noun are equally common among OV languages" (p118). Independently, Huang [START_REF] Xing | Woguo shaoshu minzu yuyan de cixu leixing' (The Word Order typology of minority languages in China)[END_REF] statistics based on 35 non-Han languages in China corroborate Dryer's observations. One phenomenon is striking in Huang's (1996: 12) table. In the Tibeto-Burman group, belonging to the OV language type, and the Altaic group, also of OV type, 17 languages use NNum order while no language uses NumN order. However, many Tibeto-Burman languages possess classifiers. Thus, these statistics without classifiers are more or less meaningless. The NumN or NNum order can help us better grasp the word order patterns in languages without an obligatory NumCL system. This is the case in Old Chinese (OC 11-1 st centuries BC) when classifiers were not fully developed. OC is mainly a VO language [START_REF] Shen | Yinxu jiagu buci yuxu yanjiu ( Studies on word order of oracular inscriptions on tortoise shells and bones of the Dynasty Yin ruins)[END_REF][START_REF] Peyraube | Ordre des constituants en chinois archaï que[END_REF] The order NumN (ex. 4 and 5) is most frequent, while the NNum order (ex. 6) is rare in OC (see Table 2). Table 1 also confirms the statistics of Dryer (1992: 118): VO languages exhibit a strong tendency to be NumN. How about Middle Chinese (MC), after the Chinese language had undergone a typological change [START_REF] Xu | Typological Change in Chinese Syntax[END_REF] starting in the Western Han (206 BC-23 AD)?

Word order change of Chinese nominal classifiers

According to previous scholars such as [START_REF] Li | Hanyu jianshi (Outline of the Chinese Language History)[END_REF][START_REF] Hashimoto | The genealogy and the role of the classifier in Sino-Tibetan[END_REF], [START_REF] Peyraube | Shanggu zhonggu hanyu liangci de lishi fazhan' (Evolution of classifiers in Old Chinese and Middle Chinese)[END_REF] and others, classifiers began to develop during the Han. According to the commonly accepted view, there are three steps (simplified here) illustrating the use of classifiers in the Chinese noun phrase (the symbol ">" meaning "evolve toward") :

(7) NumN > NNumCL > NumCLN Some comments are necessary to explain this change. The evolution is not linear (we will discuss this in more detail later). The schema of the first step (NumN) does not imply that NNum did not exist. This phenomenon is parallel to VO vs. OV word order in Chinese; the fact that Old Chinese was mainly a VO language does not exclude some OV order sentences, which existed but were not dominant [START_REF] Xu | Typological Change in Chinese Syntax[END_REF]. In Table 1, we saw that NumN order coexists with NNum, but the latter does not represent the prevalent word order tendency of that period. At a later time, the dominant order NumN stabilized. Table 2 is The statistics in Table 2 are self-evident. The order NumN is the most attested at that period in this excavated text. Many linguists such as [START_REF] Peyraube | Shanggu zhonggu hanyu liangci de lishi fazhan' (Evolution of classifiers in Old Chinese and Middle Chinese)[END_REF] are right to indicate that measure words were used first, and classifiers showed up later in the same slot. We distinguish measure words from common nouns in order to better see their development. Measure words like lǐ 'half kilometer', nián 'year' and yuè 'month' are most frequently seen in this text. The order NNumCL is found twice. This is due to the text's style. In the same tomb, other texts about medicine were excavated. According to Zhang Junzhi and Zhang Xiancheng (2002: 220), the order NNumCL/MW is attested more than 100 times in the 五十二病方 Wǔshí'èr bìng fāng 'fifty-two prescriptions' (almost the same period as the ZZJ). It is unfortunate that the authors did not distinguish measure words from classifiers. In fact, more than 60% measure words in their data are included in their statistics. In any case, their studies confirm that the order NNumCL began to develop around the Han period 5 Now let us observe statistics from other scholars. The following table suggests that the order NumN (with some NNum) lasted at least until the Tang, while the order NNumCL began to develop in the Han and coexisted with NumN. In other words, the development was not linear from the first stage to the second stage, but with overlaps. The boundary between the second and third steps (NNumCL>NumCLN) does not appear to have taken place earlier than the Tang. Studies by Wang [START_REF] Li | Hanyu jianshi (Outline of the Chinese Language History)[END_REF], [START_REF] Hashimoto | The genealogy and the role of the classifier in Sino-Tibetan[END_REF], Peyraube and Wiebusch (1993), Sun Yan (2000), Wu [START_REF] Wu | Hanyu shuliang jiegou yuxu yanbian de lishi kaocha (Diachronic Investigations on Word Order Change of Numeral Classifiers in Chinese)[END_REF] and [START_REF] Fuxiang | Wei-Jin Nanbei Chao shiqi hanyu mingliangci fanchou de yufahua chengdu[END_REF] converge to the same conclusion. Consider the following table by Wu Fuxiang (2006: 559) The independent observations of Sun Yan (2000: 407) based on a text from the late Tang confirm the above statistics, i.e. NNumCL is attested more than NumCLN even though the two orders coexisted. All of these studies show that the Chinese language became a NumCL language after the Tang Dynasty, and the order NumCLN won as a dominant order only around the 13th century AD.

Monographs and articles on classifier development are numerous. Scholars note that fully-fledged classifiers are almost all monosyllabic. At the first step, echo classifiers are found on bone inscriptions. Many Tibeto-Burman languages still use echo classifiers. [START_REF] Yuming | Kaobeixing liangci jiqi zai Han-Zang yuxi liangci fazhan zhong de diwei' (Echoclassifiers and their role in classifier development in Sino-Tibetan)[END_REF] indicates that this type of classifier is a primitive phase in classifier development. We can say at least that the reverse process, i.e. a classifier becoming an echo classifier, is not reported. When general classifiers are formed or become mature, echo classifiers become restricted and eventually disappear. As scholars have pointed out, measure words were first used with numerals, and by analogy classifiers took the same position later in noun phrases. We will not deal with all these details in this paper.

Development of verbal classifiers compared with nominal classifiers

In some numeral classifier languages, verbal classifiers are also attested. In general, verbal CL develop after nominal CL and are apparently much less numerous. Now we examine how verbal classifiers evolved in Chinese and compare its development with nominal classifiers. It is a well known fact that in Chinese verbal classifier is obligatory and shows in postverbal position, as in VNumCL. But it did not start this way. Scholars agree in general 7 that verbal classifiers develop in these three steps:

(14) NumV > VNum > VNumCL
Again, each step is not without some exceptions, but the main tendency is illustrated by these steps. According to several different studies, the order NumV was dominant before the Han: A few instances of the order VNum are also found (cf. Tang Yuming [1990[START_REF] Yuming | [END_REF]. Here is a table illustrating verbal quantification expressions in OC, from Tang Yuming ([1990], 2002: 203). Bianwen (p. 127). Is it due to the style of these texts or other factors? It is worth noting that in the texts of Dunhuang, the order 'Num CL N' is more frequent than 'N Num CL ', i.e. 375 vs. 246 (pp. 110-111). It seems that the word order was undergoing changes during this period.

(15) 吾 日 三 省 吾 身 (論語.
It is clear that the occurrences of NumV represent the predominant order in OC while a few instances of VNum can be seen. In the earliest examples with VNum given by Tang, we notice that in most of them (7 out of 10) the verb is limited to 笞 chī 'flog, beat with bamboo stick', or 鞭 biān 'flog'. This finding is further confirmed by the statistics of Wen Desheng (2000: 127-128) from the 睡虎地秦墓竹簡 Shuì hǔ dì Qín mù zhújiǎn (SHD), an excavated text on bamboo slips dated from around the 3rd century BC. Wei noted that there are six instances of VNum order, all with the verb 治(笞) chī 'flog'. The order NumV, in contrast, is used 17 times. Here is an example with VNum order given by Tang in OC:

( Parentheses mean that the order began to exist. The absence of some orders such as NNum or VNum does not imply that they did not exist, but they were not representative at these periods. In comparing classifier development in Chinese, we notice that nominal CLs and verbal CLs began to develop from the same origin but ended up in different places:

(19) NumN > NNumCL > NumCLN NumV > VNum> VNumCL
Table 6 shows that (1) At the beginning, Num preceded either N or V;

(2) The verbal CL began to develop when CL was fully-fledged in the NP;

(3) The order NumCL in NPs became prenominal, while NumCL in a VP remained in the postverbal position.

The development of classifiers in Chinese may lead us to conclude that nominal classifiers develop before verbal classifiers in NumCL-obligatory languages. It is interesting to see that the distribution of nominal CL and verbal CL are complementary. Sun Hongkai (1988: 351), Tang Yuming ([1990], 2002: 206) and Shi Yuzhi (2006: 192-193) have already noted this phenomenon. We will add some pieces of evidence to contribute to the discussion.

Cross-linguistic complementary distribution of nominal classifiers and verbal classifiers

In section 3, we showed that nominal classifiers and verbal classifiers ended up taking complementary positions in Chinese syntax. One point has to be noted: at the beginning, their distribution was not complementary. A numeral could precede a noun as well as a verb; and NumCL started out at the same side of noun or verb: post nominal and post verbal. Now let us observe the distribution of nominal CL and verbal CL in non-Han languages and in cross-linguistic data. As we have just mentioned above, scholars noticed the complementary distribution of nominal classifiers and verbal classifiers in Tibeto-Burman languages and in the history of Chinese. Here we provide a larger sample of languages, which goes beyond Tibetan-Burman languages to include Altaic and Austro-Asian languages. A linguistic map of languages of China is provided as Appendix I at the end. The classification of languages in Table 7 is from 中國的語言 Zhōngguó de yǔyán (2007). Languages are chosen more or less randomly in one subgroup; recently studied languages and less-known languages have also been added. The list is not exhaustive. In Tibeto-Burman, most groups from Tibetan, Yi, Jingpo and Qiang are represented here. Some languages belong to the Tai (Dong-Tai) and Hmong-Mien (Miao-Yao) groups, as well as the Altaic and Austro-Asiatic families. We can observe the following based on Table 7: 1. The VO or OV order is pertinent for language subgroups (correlates with NumCL and N order) except Bai and Dai (Dehong). Two OV patterns are found, in Tibetan-Burman and Altaic. Two VO patterns are also attested, in Tai-Hmong Mien and Austro-Asiatic. In the Altaic languages, the Mongolic group is absent because it seems that this group does not use CL (measure words are excluded here); a numeral can directly modify a noun. 2. The Num+CL group shows up in the reverse order with N and V respectively, whereas the internal order of the group remains constant (rare exceptions for numeral 1, see also [START_REF] Shi | Yufahua de dongyin yu jizhi (Motivation and Mechanism of Grammaticalization)[END_REF]. More precisely, if nominal CLs are on the right of nouns in a language, verbal CLs will be on the left of verbs, and vice versa, regardless of the internal order of Num and CL. According to Sun Hongkai (1988: 341), classifiers are not abundant in languages in which the CL precedes the Num. [START_REF] Qingxia | Mengya qi liangci de leixingxue tezheng-Jingpo yu liangci de ge'an yanjiu (Typological characteristics of classifiers at a primitive stage-the case of Jingpo), Studies on Sino-Tibetan languages: Papers in honor of Professor Hwang-Cherng Gong on his seventieth Birthday[END_REF] article confirms that classifiers in the Jingpo language -having a CLNum order in the NP -are at a very primitive stage. In OV languages, NumCL in Yi and Qiang groups and CLNum in Tibetan and Jingpo groups tend to be postnominal and preverbal. VO languages, except the dialect of Dai cited in the table and some Austro-Asiatic languages, clearly prefer the NumCL order. NumCL occur in prenominal and postverbal position in most of the VO languages studied. 3. Four patterns of the complementary position of classifiers are seen in Table 7. 4. Some exceptions exist for the complementary position of classifiers. The Bai language has NumCL order to the right of both noun and verb. In the Dai dialect (Dehong), the distribution is not neat either. NumCLN and NumCLV coexist in Korean, an OV language, and in Buxing, Kemu and Bugeng, three VO languages of the Austro-Asiatic family according to scholars' descriptions (see Table 7). The Buxing or Kemu speakers have close contact with Dai people. This may provide us an explanation why Dai and these languages do not present a complementary distribution of classifiers. In these languages, word order may be continuing to change due to complex contacts between languages.

Discussion

In section 4 we saw that in some languages, against the general trend, nominal and verbal classifier distributions are not in complementary positions. We propose that if in one language a nominal CL and a verbal CL are on the same side with respect to a noun or to a verb, then classifiers in this language should be in a developing stage. This could be the situation in Bai, which is influenced by Chinese and always presents atypical characteristics in the Yi group. In other words, we think that Bai is still undergoing transition in terms of word order change in regard to numeral classifiers. In some Austro-Asiatic languages, two orders often coexist; this also suggests that a word order change is taking place. We hope that further studies of these languages will shed light on this issue.

We have looked at Chinese classifier evolution to try to understand the reason why nominal CL and verbal CL tend to be in opposite positions in most languages. Table 6 shows that the orders NNumCL/NumCLN and VNumCL coexisted during the Wei-Jin, and only from the Tang did nominal NumCL and verbal NumCL become complementary. Is the phenomenon found in contemporary Austro-Asiatic languages and in some Dai dialects parallel to the evolution of classifiers in Middle Chinese?

In fact, when nominal quantification and verbal quantification take the same form, i.e. at the same side of a noun or verb, confusion is possible: This example is cited by Ye [START_REF] Guichen | Hanyu dongliangci xingcheng de yuanyin' (On the formation of verbal classifiers in Chinese)[END_REF]. The authors argue that verbal CLs were formed to distinguish themselves from nominal quantification 8 . Here the NP "read-poem-three-hundred" refers to the first Odes Shījīng which contains 305 poems. But as Ye and Luo pointed out, nothing in this phrase's syntax would prevent interpreting "three-hundred" as verbal quantification ('three hundred times'). The following example is used by Tang Yuming ([1990] This example shows that if nominal CL and verbal CL take the same syntactic position (both at the same side of a noun or of a verb), ambiguities may arise. Tang cited [START_REF] Shiru | Weijin Nanbei chao liangci yanjiu[END_REF] who had indicated that the word 匝 zā 'circuit' is a nominal classifier of 城 ché ng 'city' rather than a verbal classifier of the verb 围 wé i 'surround'. One can suggest that possible confusions between a nominal CL and a verbal CL require readjustment of word order.

The Bai language is another language with such a possible, but unrealized confusion. In a string of words Verb-Noun-CL-Num, it is possible to interpret CL-Num as part of noun phrase or as verbal modifier. However, there are no ambiguous classifiers in the language, at least we have not found any ambiguous classifier in Bai.

In conclusion, two possibilities explain the non-complementary distribution of nominal CLs and verbal CLs in some languages. (1) The language has yet to complete a word order change during a historical stage; (2) There is no chance of confusion when nominal CL and verbal CL are on the same side of a noun or verb. However, nominal classifiers and verbal classifiers present a word order in complementary distribution in most languages investigated in our paper.

8

We do not agree with their assertion that verbal CLs were already being used in the Qin Dynasty. 9 O.M. represents object marker.

  a summary of the distribution of NumN, NNum and NNumCL based on an excavated text of the 戰國縱橫家書 Zhànguó zònghéngjiā shū (ZZJ + 195BC, hereafter ZZJ).

  (a) Tibetan-Jingpo type: NCLNum and CLNumV. (b)Yi-Qiang type: NNumCL and NumCLV (c)Tai (Dong-Tai) and Hmong-Mien (Miao-Yao) type: NumCLN and VNumCL. (d)Mixed type: distribution of Num and CL is less neat. This is displayed in some Austro-Asian and Altaic languages. Two subtypes, (a) and (b), can be distinguished for OV languages. Likewise, VO languages have two subtypes, namely (c) and (d). Contemporary Chinese (Mandarin) belongs to type (c).

  [the army of Liu Bang] circled the City of Wan three times/ in three concentric circles.

  several NCL "To Dad, Mom said a few sentences." (23) ɑ 31 ti 33 ŋv 55 ɑ 31 mo 33 suɑ 44 lɑ 42 to 21 kɑ 33 tɑ 21 Dad O.M. mom speak Past speech several VCL "To Dad, mom spoke several times."

  To give examples in Chinese, in (1), the noun hua 'flower' is modified by Num+CL, the different classifiers used give a different meaning: while zhi refers to flowers with a stem duo only refers to the flower itself.

	(1) a. 三枝花
	sān zhī huā
	three CL flower
	'three (single stem) flower'
	b. 三朵花
	sān duǒ huā
	three CL flower
	'three flowers (without the stem)'
	In (2), we have examples of measure words:
	(2) a. 三碗水
	sān wǎn shuǐ
	three MW water
	'three bowls of water'
	b. 三桶水
	sān tǒng shuǐ
	three bucket water
	'three buckets of water'
	While all languages have measure words of some sort, few have numeral
	classifiers. The term 'verbal classifiers', is used differently here. It is sometimes used
	as verbal affix referring to predicate argument

See the following table established by Wu Dan (2005): Table 1. NumN and NNum in Old Chinese

	(4) 三 人	行, 必	有	我	師	焉(論語.述而)
	sān	ré n	xí ng, bì	yǒu	wǒ	shī	yān( Lúnyǔ. Shù é r)
	three man walk, certain have my	master final-particle
	Walking with two persons, I must have a teacher among them.
	(5) 拔	二 城(戰國縱橫家書. 25 章 3 )
	bá	è r	ché ng(Zhànguó zònghéngjiā shū. 25)
	conquer two city [Jing Ji] has conquered two cities.
	(6) 大縣 十七(戰國縱橫家書. 26 章)
	dà xiàn shíqī(Zhànguó zònghéngjiā shū. 26)
	county seventeenseventeen counties
			among others). Does this NumN & VO pattern work
	for OC? NumN		NNum
	詩經 Shījīng 11 th -6 th centuries BC	25		5
	尚書 Shàngshū 5 th century BC?	22		0
	論語 Lúnyǔ 5 th century BC	4			1
	左傳 Zuǒ zhuàn 5 th century BC 2	54		6
	孟子 Mèng Zǐ 4 th century BC	35		7
	Total			140		19
	In this table, the order of NumN and NNum is significant, since at that period
	classifiers did not exist as a system. It is clear that the NumN order is predominant.
	NNum existed, but the proportion of its occurrence is only about one in seven.
	Consider these examples in OC in which the numeral precedes the noun:

Table 2 .

 2 NumN and NNum and NNumCL in the ZZJ (+ 195BC) Excluded from this table are proper nouns such as 三晉 Sān Jìn,三梁 sān Liáng and so forth. The word 乘 shè ng 'chariot' is different from other measure words. It can be used as a noun (8 occurrences) and classifier (twice). The only two examples of NNumCL involve shè ng:

	N and Measure Word 4	NumN	NNum	NnumCL

  Recent studies such as SunYan (2000), Wu[START_REF] Wu | Hanyu shuliang jiegou yuxu yanbian de lishi kaocha (Diachronic Investigations on Word Order Change of Numeral Classifiers in Chinese)[END_REF],[START_REF] Fuxiang | Wei-Jin Nanbei Chao shiqi hanyu mingliangci fanchou de yufahua chengdu[END_REF] among others show that the order NumN without classifier was the dominant order until the Tang Dynasty (618-907). According to Wu Dan andWu Fuxiang (2006: 556-557), during 5th century AD, NNum or NumN 6 without a classifier made up 90% of cases in transmitted texts. This situation remained the same until the Yuan Dynasty (1271-1368). It is clear that the situation drastically changed beginning in the Yuan, as indicated in Table3below. In other words, classifiers became obligatory much later than current studies suggest. Here are two examples from transmitted texts:

	(10)		烏豙(喙) 十四 果(顆)(五十二病方)
	wū yì (huì )	shí sì	guǒ(kē)(Wǔshí'èr bìng fāng)
	aconitum	fourteen CL
	fourteen aconitum
	(11)			龍須(鬚)	一	束(五十二
	病方)
	lóng xū(xū)		yī	shù
	rush			one	CL
	one bundle of rush
	(12)	出一編書 (史记 55)
	chū yī biānshū (Shǐjì)
	take out one CL book
	[He] took out one book.
	(13)	馬三匹(左傳.莊公 16)
	mǎ sān pǐ (Zuǒ zhuàn. Zhuāng gōng 16)
	horse three CL
	three horses
					. Observe
	two examples drawn from this excavated text.

Table 3 .

 3 Proportion of noun phrases (NP) without CL to NP with CL (by[START_REF] Fuxiang | Wei-Jin Nanbei Chao shiqi hanyu mingliangci fanchou de yufahua chengdu[END_REF] based on Wu Dan 2005)

	Periods	N Num and Num N	N Num CL and Num CL N
		(without CL)
		(figures represent relative frequency, not tokens)
	先秦 Xiān Qín	10	1
	ca. 8th-3rd c. BC
	漢代 Hà n dà i 206 BC-220 AD	9	1
	魏晉南北朝 Wè i-Jì n Ná n-Běi-	10	1
	Chá o ca. 3rd-6th c. AD
	唐代 Tá ngdà i 618-907	4	1

6

The authors did not give the statistics on either NumN or NNum.

Table 4 .

 4 based on Wu Dan (2005): Relative frequency of NumCLN and NNumCL

	Periods	Num CL N	N Num CL
	先秦 Xiān Qín ca. 8th-3rd c. BC	1	5
	漢代 Hàn dài 206 BC-220 AD	1	3
	魏晉南北朝 Wè i-Jì n Nán-Běi Cháo	1	1
	ca. 3rd-6th c. AD
	唐代 Tángdài 618-907	5	1
	宋代 Sòngdài 960-1279	9	1
	元明清 Yuán Míng Qīng 1271-1911	15	1

Table 5 .

 5 NumV and VNum in Old Chinese

	NumV	VNum

7

Hong

[START_REF] Yifang | Dunhuang Tulufan wenshu zhong zhi liangci yanjiu[END_REF]

notes the order 'Num CL V' in her data. This order appears twice in the texts of Tulufan (4th-8th centuries) (p.69), while in the texts of Dunhuang (8th-10th centuries), it occurs half of the time of the 'V Num CL' order, i.e. 33 'Num CL V' (p.129) vs. 61 'V Num CL' in the Dunhuang

Table 6 .

 6 In example (17), the order VNum is used. But this order is not frequent in OC. Real verbal CLs are found in the Wei-Jin period. Observe example (18): Synthesis of the nominal CL and verbal CL development

	17)		當	笞			五十(睡虎
	地秦墓竹簡)
			dāng	chī			wǔshí(SHD
	)
			must	beat.with.bamboo.stick	fifty
	This merits fifty beatings with a bamboo stick.
	(18)			讀	書	百	遍	而
				義	自	見。(三國志)
				dú	shū	bǎi	biàn é r yì
				zì	xiàn. (Sānguó zhì)
				read	book hundred	CL
				Conj meaning self to become visible ?
	Reading a book one hundred times, the meaning itself becomes clear.
	In Table 6 we have roughly sketched classifier evolution in Chinese:
	先秦	漢代	魏晉	唐宋	元
	Xiān Qín	Hàn dài	Wè i-Jì n	Táng Sòng	Yuán
	NumN	NumN	NumN	NumN	NumN
	(NNumCL) NNumCL	NNumCL/	NumCLN	NumCLN
			NumCLN
	NumV	VNum	VNumCL	VNumCL	VNumCL
		(VNumCL)

Table 7 .

 7 Complementary positions of classifiers in cross-linguistic data

	Languages VO/	NumCLN	other	VNumCL other	Sources
	OV	NNumCL	orders	NumCLV orders
	Tibeto-

Burman groups of Sino-Tibetan languages

	Buni	VO	NumCLN		VNumCL	Mao and Li
	(Jiongnai)					2002
	Altaic languages
	Salar	OV	NNumCL	NNum	NumCLV NumV	Lin 1985
	(Sala)		NumCLN
	Korean	OV	NNumCL	NNum	NumCLV NumV	Jin 2005
			NumCLN	NumN
	Manchu	OV	NNumCL NumN	NumCLV	Wang 2005
	Austro-Asiatic languages
	Kemie	VO	NumCLN echo CL	VNumCL	Chen 2005
	Mang	VO	NumCLN CLN when	VNumCL VCLNu	Gao 2003
				Num=1	m
					when
					Num=1
	Gin (Jing) VO	NumCLN		VNumCL	Ouyang et al.
						1984
	Bolyu	VO	NumCLN		VNumCL	Li XL. 1999
	(Lai)
	Bugan	VO	NumCLN		VNumCL	Li YB. 2005
	(Bugeng)		NNumCL
	Buxing	VO	NumCLN		VNumCL	Gao 2004
			NNumCL
	Khmu	VO	NumCLN		VNumCL	Chen 2002
	(Kemu)		NNumCL
	Tibetan
	Maqu	OV	NCLNum		CLNumV	Zhou 2003
	Zang
	Cangluo	OV	NCLNum NNum	CLNumV	Zhang 1986
	Menba	OV	NCLNum NNum	CLNumV	Lu 2002
	Baima	OV	NCLNum NNumCL CLNumV	Sun 2007
	Yi (Lolo)
	Yi (Xide)	OV	NNumCL		NumCLV	ZGDYY 2007
	Lahu	OV	NNumCL		NumCLV	Chang et al.
						1986
	Naxi	OV	NNumCL echo CL :	NumCLV	He & Jiang
				N1NumN		1985
				2
	Sangkong OV	NNumCL		NumCLV	Li YS. 2002
	Kazhuo	OV	NNumCL		NumCLV	Mu 2003
	Rouruo	OV	NNumCL		NumCLV	Sun et al.

The statistics could vary: Wu Dan excludes postnominal numerals which can be interpreted as verbs.

戰國縱橫家書 Zhànguó zònghéngjiā shū (ZZJ + 195BC) [Letters of Strategists in the Warring States period].

Measure words (MW) exist in all languages such as 'a cup of tea' in English or 'une tasse de thé' in French. These words helped the development of classifiers in Chinese but they must not be considered as classifiers. In this paper we distinguish MW and CL. Tables based on other scholars' works does also make this distinction.

The study of WeiDesheng (2000: 128) shows the same tendency, NNumCl order is not rare in the 睡 虎地秦墓竹簡 Shuì hǔ dì Qín mù zhújiǎn, an excavated text on bamboo slips dated from around the 3rd century BC.


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WP2 User Requirements & Benchmarking of Key Competencies Deliverable 7: Report on user Requirements: Reference Curricula to be Developed and Benchmarking Key Criteria

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Introduction

The design and implementation of a platform-based training course requires an understanding of basic concepts from psychology, education, and human-computer interaction which are all essential to the development of successful learning environments.

It may not be immediately evident, but a carefully designed learning environment benefits more than one stakeholder, including instructors, students, the general public, and other external parties. On the other hand, poor interface design can become a serious obstacle to learning outcomes, as it may impose cognitive obstacles. Indeed, the more of the brain the user has to allocate to the interface, the less is available for learning (see Fig. 1), which is the contrary to what one wants their users to do; ie to devote their concentration and attention to the learning process. [1] [1] Peters, Dorian. Interface Design for Learning: Design Strategies for Learning Experiences. San Francisco: New Riders, 2014, p.66 Learnability -that is the capability of a software product to enable the user to learn how to use it-is also, along with usability, absolutely essential when it comes to software and learning environments. Learnability is all about easily mastering the software without instruction, not about learning the content presented, which, in turn is essential in controlling or reducing the learning curve a user must face and overcome before they can focus their attention to the learning process. In contrast to learnability, interface design for e-learning examines how interfaces can support learning in general, whether it's learning about how to build and expand ontologies or use software-enabled textual analysis.

The Empirical Research

A qualitative analysis and interpretation of online teaching practices and recommendations in the domain of the Digital Humanities and the elicitation of corresponding user requirements for this report was based on a series of semi-structured interviews with experienced instructors of online courses in the broader Digital Humanities field from Europe. Fifteen interviews were conducted between May 2015 and October 2015, either face-to-face or via Skype. Interviews were carried out mainly in English, however two of them were conducted in Greek and were later translated in English. Interviewees were instructors carrying out syllabus design and teaching, preferably online, in the Digital Humanities and related areas. Among the reasons for the selection of these particular interviewees was their expertise and affiliation with research institutes or academic departments. All interviews were recorded with the consent of the interviewees.

The duration of the interviews ranged from forty minutes to one and a half hours, depending on the interviewees' personal interests, area of research, as well as their familiarity with online training courses, which is an area of particular importance for #dariahTeach. The semistructured design of the interviews encouraged a conversational tone, as well as facilitated raising a variety of topics which the participant considered important to his or her teaching activity.

Interviewees were at different career stages, ranging from doctoral candidates / early career instructors to full professors, while all of them held academic-related positions. They displayed varying familiarity with and experience of online teaching. Nine of the interviewees were male, the rest female. Geographically, the interviews covered participants from the U.K., Ireland, Greece, Portugal, Spain and France.

List of interviewees

Interview Codebook

The typical interview scenario consisted of a short introduction about #dariahTeach and its goals followed by a set of open questions regarding both conventional and online training courses, teaching syllabi, technical expectations, narratives and expected outcomes. Questions were organised as indicated by the themes presented in the following tables: "What I found absolutely annoying is 95 pages of pdf for a class. We did not even have access to .pdf so we had to copy/paste and I had to quit. I never finished it. And it was the only resource. I went through it with keywords. And then on the Facebook page of the class I told them, don't read from page so-so to page so-so, there is nothing important.

So don't start with a difficult thing from the beginning. Start with tasks that help people to get to know the platform and each other and then little by little complicate things."

"For TEI online training material, what I found good about it was that it was fairly generic, it was quite well-written and it could be applied to multiple situations. What I found it did not work for digital humanities training materials is any attempt to personalize them. I think there should be a methodological focus, things need to be quite basic, quite generic."

Table 3 Theme Details

The Modules This key theme pertains to the structure of the modules and each unit within them. Issues of module and unit independence and length are also raised. Interviewees were asked about the importance of stating the learning outcomes of each module, and each unit within the module, as well as of indications of different levels of complexity within the module or the units.

Example "Not all modules should be of the same complexity. "The platform should have tools that would allow the users to do exercises online and have some kind of feedback.

Other general tools could be on bibliography, be able to download references connected to a unit in whatever format based on the user's repository of references (e.g. Endnote).

Modules designed to be developed in #dariahTeach should point to relevant tools that already exist as much as possible."

The Findings

In the following section, requirements are broken down into three main categories: The Platform, The Modules and Other, although these categories often overlap. The list of User Requirements that emerged from the interviews were enhanced and refined by a series of focus group held in Amsterdam, Copenhagen and London in 2015. These meetings explored the issue of online teaching and training of Audio Visual material and were organized by project partners from Aarhus, Lausanne, and Rotterdam. The questions used in these focus groups can be found in Appendix I.

Each User Requirements category has a number of specific requirements. These requirements emerged multiple times during different interviews and correspond to the most popular suggestions of the interviewees. While there has not been any attempt to rank the popularity or value of each requirement, the requirements presented here are considered significant for multiple DH instructors. This document was not designed to be the basis for the development of functional specifications. The Project should analyze and evaluate both the individual features outlined below and the overall environment in terms of a coherent service, taking into consideration future growth and sustainability, as well as systemic weaknesses or limits.

I. The Platform

Design and features of the platform

 The Platform should be adaptable to different learning methodologies.

 The Platform should enable rich assessment.

 The Platform should be accessible, in the broadest sense of the word.

 The Platform should not be isolated.

 The Platform should not be complex and it should be transparent.

 The Platform should be user friendly to the maximum  The Platform should not necessarily be aesthetically appealing.

 The Platform should be more focused on building a community rather than on design.

 The Platform should not have static information, not a repository-like platform.

 The Platform should be a free-structure environment ("Like a blog with semantic capabilities").

  The Platform should be solid and robust.

 The Platform should be user-tested during its development.

 The Platform should include alternative ways to FAQS e.g. little bubble that says "you should click here" etc.

Collaboration

User interaction

 The Platform should allow for persistent roles (set the role, such as instructor, student, observer, etc. in the authentication/authorization and it is respected in the environment and plugged-in applications).

 The Platform should function as a sandbox in which students can experiment with the material presented.

 The Platform should be flexible and have features such as Amazon-type "you may like this" element.

 The Platform should host user profiles to encourage visibility of users' work.

Content Features

 The Platform should include PDFs to download.

 The Platform should be editable having open document format.

 The Platform should support ad hoc groupings.

 The Platform should support grouping of materials across modules and units.

Implementation

 The Platform should be flexible, allowing users or different groups to plug in or link to tools that fulfill particular needs, if built-in tools do not provide the desired functionality.

 The Platform should provide an API or advanced forms of web services so that new/unforeseen components can be added to the environment.

 Specifics could include one or more of the following: plug-in architecture for third-party assessment modules, integration with assignments, assessment tools.

 The Platform should support user customization. Specifics could include personalized portal page and/or integration with appropriate other tools, such as Facebook (if

II. The Modules

Content and Features

 The Modules should provide foundation, theoretical courses on Digital Humanities as well as, where appropriate, should offer block courses on basic Computer Science skills.

 Some units within modules should be on background theory, while the rest should be more hands-on / practical. Both theoretical and more practical units should be included.  For modules and teaching material to be incorporated in other people's classes, they should be exportable to learning platforms such as Blackboard and/or written in XML or HTML.

 The Modules should make material openly and freely available allowing students to have access to it after they have left. Copyright should be clear and shareable. Provenance of the material should be also clearly stated.

 The Modules and teaching material should be exportable to other learning platforms to allow interoperability.

 If modules and units are to be adapted/copied by other universities rights issues should be clear.

Search features

 Modules should allow for serendipitous search allowing users to find something they had not thought of.

 Modules should provide the ability to search in different ways, not just keywords for topics but also for formats.

Structure

 Module units should not be absolutely standalone: They should follow a mixed approach, in which the first one to three units should be required. Furthermore, suggested pathways across units should be provided.

 Module units should be created as separate entities, providing the ability to be integrated separately into a learning environment where users would be able to follow their own learning pathways.

Length

 Modules should ideally last from ten to fourteen teaching weeks.

 Modules should follow format of semesters and thus be clear and familiar.

Learning outcomes

 Learning outcomes should be explicitly stated at on course level, not necessarily on unit level: students should be made aware of what they are expected to perform with goals clearly stated.

Levels of complexity

 Complexity should be more intense as the module progresses but all modules should begin at the beginners' level: there should be evaluation based on the different level of difficulty of solutions users apply in their assignments.

Learning object metadata

 Modules should cater for dynamic curation of learning object metadata.

III. Other

 Τhe community element of developing a shared resource should be highlighted and addressed as an issue of great significance, as it is generally missed from open education resources.

  Figure 1.

  The Platform should have clear statement of what users can but mainly what they cannot do in the platform/with tools.



  Assignments should be developed to teach students how to understand online archives and collections as well as how to explore them and develop a research question in relation to exploring content. Students often start with a research question and then try and find material -and fail. Developing research 'in dialogue' with (re)searching content is a foreign trajectory for many.



  The Platform should enable synchronous collaboration and communication: users must be able to work together over distance. Specifics could include one or more of the following: document sharing, desktop and application sharing, voice over Internet, instant messaging, video over Internet, web conferencing that integrates some or all of the above. The Platform should enable asynchronous collaboration and communication. Specifics could include one or more of the following: outgoing email to entire class or specific individuals or groups, threaded web-based discussion boards, workgroup work spaces, or subsites, wikis, blogs, document repositories, workflow (task management), group calendaring.

 The sustainability of the platform should be ensured through DARIAH.

 In order for users to be encouraged to publish training material in such a platform they should have sense of the platform's sustainability, a, sense of curation and of feedback in response to the developed material. Can you say something about the degree of digital literacy of your students?

Appendix I #dariahTeach -DH curriculum -Module on Audiovisual Media and Multimodal Literacies

What are the most frequent obstacles and problems when teaching about AV at your university?