Статті в журналах з теми "Flamelet theory"

One basic effect of turbulence in turbulent premixed combustion is for the fluctuating velocity field to wrinkle the flame and greatly increase its surface area. In the flamelet theory, this effect is described by the flame surface density. An exact evolution equation for the flame surface density, called the Σ-equation, may be written, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly. Direct numerical simulation (DNS) is used in this paper to estimate the different terms appearing in the Σ-equation. The numerical configuration corresponds to three-dimensional premixed flames in isotropic turbulent flow. The simulations are performed for various mixture Lewis numbers in order to modify the strength and nature of the flame-flow coupling. The DNS-based analysis provides much information relevant to flamelet models. In particular, the flame surface density, and the source and sink terms for the flame surface density, are resolved spatially across the turbulent flame brush. The geometry as well as the dynamics of the flame differ quite significantly from one end of the reaction zone to the other. For instance, contrary to the intuitive idea that flame propagation effects merely counteract the wrinkling due to the turbulence, the role of flame propagation is not constant across the turbulent brush and switches from flame surface production at the front to flame surface dissipation at the back. Direct comparisons with flamelet models are also performed. The Bray-Moss-Libby assumption that the flame surface density is proportional to the flamelet crossing frequency, a quantity that can be measured in experiments, is found to be valid. Major uncertainties remain, however, over an appropriate description of the flamelet crossing frequency. In comparison, the coherent flame model of Marble & Broadwell achieves closure at the level of the Σ-equation and provides a more promising physically based description of the flame surface dynamics. Some areas where the model needs improvement are identified.

Premixed turbulent combustion in the flamelet regime is analysed on the basis of a field equation. This equation describes the instantaneous flame contour as an isoscalar surface of the scalar field G(x,t). The field equation contains the laminar burning velocity sL as velocity scale and its extension includes the effect of flame stretch involving the Markstein length [Lscr ] as a characteristic lengthscale of the order of the flame thickness. The scalar G(x,t) plays a similar role for premixed flamelet combustion as the mixture fraction Z(x,t) in the theory of non-premixed flamelet combustion.Equations for the mean $\overline{G}$ and variance $\overline{G^{\prime 2}}$ are derived. Additional closure problems arise for the mean source terms in these equations. In order to understand the nature of these terms an ensemble of premixed flamelets with arbitrary initial conditions in constant-density homogeneous isotropic turbulence is considered. An equation for the two-point correlation $\overline{G^{\prime}({\boldmath x},t)G^{\prime}({\boldmath x}+{\boldmath r},t)}$ is derived. When this equation is transformed into spectral space, closure approximations based on the assumption of locality and on dimensional analysis are introduced. This leads to a linear equation for the scalar spectrum function Γ(k,t), which can be solved analytically. The solution Γ(k,t) is analysed by assuming a small-wavenumber cutoff at k0 = lT−1, where lT is the integral lengthscale of turbulence. There exists a $k^{-\frac{5}{3}}$ spectrum between lT and LG, where LG is the Gibson scale. At this scale turbulent fluctuations of the scalar field G(x,t) are kinematically restored by the smoothing effect of laminar flame propagation. A quantity called kinematic restoration ω is introduced, which plays a role similar to the scalar dissipation χ for diffusive scalars.By calculating the appropriate moments of Γ(k,t), an algebraic relation between ω, $\omega,\overline{G^{\prime}({\boldmath x},t)^2}$, the integral lengthscale lT and the viscous dissipation ε is derived. Furthermore, the scalar dissipation χ[Lscr ], based on the Markstein diffusivity [Dscr ][Lscr ] = sL [Lscr ], and the scalar-strain co-variance Σ[Lscr ] are related to ω. Dimensional analysis, again, leads to a closure of the main source term in the equation for the mean scalar $\overline{G}$. For the case of plane normal and oblique turbulent flames the turbulent burning velocity sT and the flame shape is calculated. In the absence of flame stretch the linear relation sT ∼ u′ is recovered. The flame brush thickness is of the order of the integral lengthscale. In the case of a V-shaped flame its increase with downstream position is calculated.

A method is presented to significantly improve the convergence behavior of batch nonpremixed counterflow flame simulations with finite-rate chemistry. The method is applicable to simulations with varying pressure or strain rate, as it is, for example, necessary for the creation of flamelet tables or the computation of the extinction point. The improvement is achieved by estimating the solution beforehand. The underlying scaling rules are derived from theory, literature, and empirical observations. The estimate is used as an initialization for the actual solver. This enhancement leads to a significantly improved robustness and acceleration of batch simulations. The extinction point can be simulated without cumbersome code extensions. The method is demonstrated on two test cases and the impact is discussed.

Distributed combustion, often associated with the low-oxygen condition, offers ultra-low NOx emission. However, it was recently achieved without combustion air dilution or internal flue gas recirculation, using a distinct approach called mixture temperature-controlled combustion. Here, the fuel–air stream is cooled at the inlet to delay ignition and, hence, foster homogeneous mixture formation. This numerical study aims to understand its operation better and present a robust framework for distributed combustion modeling in a parameter range where such operation was not predicted before by any existing theory. Further, liquid fuel combustion was evaluated, which brings additional complexity. Four operating conditions were presented at which distributed combustion was observed. The reacting flow was modeled by flamelet-generated manifold, based on a detailed n-dodecane mechanism. The Zimont turbulent flame speed model was used with significantly reduced coefficients to achieve distributed combustion. The droplets of airblast atomization were tracked in a Lagrangian frame. The numerical results were validated by Schlieren images and acoustic spectra. It was concluded that the reactant dilution ratio remained below 0.25 through the combustion chamber, revealing that the homogeneous fuel–air mixture is the principal reason for excellent flame stability and ultra-low NOx emission without significant internal recirculation. The potential applications of these results are boilers, furnaces, and gas turbines.

This paper extends a recent theoretical study that was previously presented in the form of a brief communication (Zimont, C&F, 192, 2018, 221-223), in which we proposed a simple splitting method for the derivation of two-fluid conditionally averaged equations of turbulent premixed combustion in the flamelet regime, formulated more conveniently for applications involving unclosed equations without surface-averaged unknowns. This two-fluid conditional averaging paradigm avoids the challenge in the Favre averaging paradigm of modeling the countergradient scalar transport phenomenon and the unusually large velocity fluctuations in a turbulent premixed flame. It is a more suitable conceptual framework that is likely to be more convenient in the long run than the traditional Favre averaging method. In this article, we further develop this paradigm and pay particular attention to the problem of modeling turbulent premixed combustion in the context of a two-fluid approach. We formulate and analyze the unclosed differential equations in terms of the conditions of the Reynolds stresses τij,u, τij,b and the mean chemical source ρW¯, which are the only modeling unknowns required in our alternative conditionally averaged equations. These equations are necessary for the development of model differential equations for the Reynolds stresses and the chemical source in the advanced modeling and simulation of turbulent premixed combustion. We propose a simpler approach to modeling the conditional Reynolds stresses based on the use of the two-fluid conditional equations of the standard “k-ε” turbulence model, which we formulate using the splitting method. The main problem arising here is the appearance in these equations of unknown terms describing the exchange of the turbulent energy k and dissipation rate ε in the unburned and burned gases. We propose an approximate way to avoid this problem. We formulate a simple algebraic expression for the mean chemical source that follows from our previous theoretical analysis of the transient turbulent premixed flame in the intermediate asymptotic stage, in which small-scale wrinkles in the instantaneous flame surface reach statistical equilibrium, while the large-scale wrinkles remain in statistical nonequilibrium.

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

Abstract Soot prediction for diesel engines is a very important aspect of internal combustion engine emissions research, especially nowadays with very strict emission norms. Computational Fluid Dynamics (CFD) is often used in this research and optimisation of CFD models in terms of a trade-off between accuracy and computational efficiency is essential. This is especially true in the industrial environment where good predictivity is necessary for engine optimisation, but computational power is limited. To investigate soot emissions for Diesel engines, in this work CFD is coupled with chemistry tabulation framework and semi-empirical soot model. The Flamelet Generated Manifold (FGM) combustion model precomputes chemistry using detailed calculations of the 0D homogeneous reactor and then stores the species mass fractions in the table, based on six look-up variables: pressure, temperature, mixture fraction, mixture fraction variance, progress variable and progress variable variance. Data is then retrieved during online CFD simulation, enabling fast execution times while keeping the accuracy of the direct chemistry calculation. In this work, the theory behind the model is discussed as well as implementation in commercial CFD code. Also, soot modelling in the framework of tabulated chemistry is investigated: mathematical model and implementation of the kinetic soot model on the tabulation side is described, and 0D simulation results are used for verification. Then, the model is validated using real-life engine geometry under different operating conditions, where better agreement with experimental measurements is achieved, compared to the standard implementation of the kinetic soot model on the CFD side.

In premixed turbulent combustion, the modelling of the turbulent flux of the mean reaction progress variable remains somewhat controversial. Classical gradient transport assumptions based on the eddy viscosity concept are often used while both experimental data and theoretical analysis have pointed out the existence of countergradient turbulent diffusion. Direct numerical simulation (DNS) is used in this paper to provide basic information on the turbulent flux of and study the occurrence of counter-gradient transport. The numerical configuration corresponds to twoor three-dimensional premixed flames in isotropic turbulent flow. The simulations correspond to various flame and flow conditions that are representative of flamelet combustion. They reveal that different flames will feature different turbulent transport properties and that these differences can be related to basic dynamical differences in the flame-flow interactions: counter-gradient diffusion occurs when the flow field near the flame is dominated by thermal dilatation due to chemical reaction, whereas gradient diffusion occurs when the flow field near the flame is dominated by the turbulent motions. The DNS-based analysis leads to a simple expression to describe the turbulent flux of , which in turn leads to a simple criterion to delineate between the gradient and counter-gradient turbulent diffusion regimes. This criterion suggests that the occurrence of one regime or the other is determined primarily by the ratio of turbulence intensity divided by the laminar flame speed, and by the flame heat release factor, τ ≡ (Tb — Tu)/Tu, where Tu and Tb are respectively the temperature within unburnt and burnt gas. Consistent with the Bray-Moss-Libby theory, counter-gradient (gradient) diffusion is promoted by low (high) values and high (low) values of τ. DNS also shows that these results are not restricted to the turbulent transport of . Similar results are found for the turbulent transport of flame surface density, Σ. The turbulent fluxes of and Σ are strongly correlated in the simulated flames and counter-gradient (gradient) diffusion of always coincides with counter-gradient (gradient) diffusion of Σ.

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

A layered description of the structure of turbulent flame brushes is provided for situations featuring large but finite values of the Damköhler number, which correspond to the wrinkled flame regime of turbulent premixed combustion. One special focus of this study is placed on the description of the leading edge of the turbulent flame brush, the role of which is known to be essential with respect to propagation, transport and stabilization issues. On the basis of rather simple and well-identified working hypotheses, the influence of slight increases in the Karlovitz number values is revealed. The phenomenology and associated statistics are also investigated analytically, which leads to a mathematical description of the leading edge internal structure. With respect to the progress variable statistics, i.e. probability density function, this leading edge can indeed be thought of as the inner part of a boundary layer where the influence of the finite thickness of laminar flamelets can no longer be neglected. From the proposed description, standard fast-chemistry closures, which are currently used to perform the numerical simulation of turbulent combustion, may easily be generalized to account for the finite-rate chemistry effects occurring in this sublayer, thus emphasizing the interest of the present analysis for turbulent combustion theory and modelling.

Skin pain resulting from mechanical compression is one of the most common pains in daily life and the indispensable information for electronic skin to perceive external signals. The external mechanical stimuli are transduced into impulses and transmitted via nerve fiber, and finally, the sensation is perceived via the procession of the nerve system. However, the mathematical mechanism for pain sensation due to mechanical stimuli remains unclear. In this paper, a mathematical model for skin pain sensation under compression is established, in which the Flament solution, the revised Hodgkin–Huxley model, and the mathematical model gate control theory are considered simultaneously. The proposed model includes three parts: a mechanical model of skin compression, a model of transduction, and a model of modulation and perception. It is demonstrated that the pain sensation degree increases with the compression amplitude and decreases with deeper nociceptor location in the skin. With the help of the proposed model, the quantitative relationship between compression pain sensation and external mechanical stimuli is revealed, which has a significant benefit in promoting the design and mechanism research of electronic skin with pain perception function.

This research uses the counter-attitudinal essay paradigm ( Janis & King, 1954 ) to test the effects of social actions on social representations. Thus, students wrote either a pro- or a counter-attitudinal essay on Higher Education. Three forms of counter-attitudinal essays were manipulated countering respectively a) students’ attitudes towards higher education; b) peripheral beliefs or c) central beliefs associated with this representation object. After writing the essay, students expressed their attitudes towards higher education and evaluated different beliefs associated with it. The structural status of these beliefs was also assessed by a “calling into question” test ( Flament, 1994a ). Results show that behavior challenging either an attitude or peripheral beliefs induces a rationalization process, giving rise to minor modifications of the representational field. These modifications are only on the social evaluative dimension of the social representation. On the other hand, when the behavior challenges central beliefs, the same rationalization process induces a cognitive restructuring of the representational field, i.e., a structural change in the representation. These results and their implications for the experimental study of representational dynamics are discussed with regard to the two-dimensional model of social representations ( Moliner, 1994 ) and rationalization theory ( Beauvois & Joule, 1996 ).

The laminar flamelet model (LFM) (Peters, 1986, “Laminar Diffusion Flamelet Models in Non-Premixed Combustion,” Prog. Energy Combust. Sci., 10, pp. 319–339; Peters, “Laminar Flamelet Concepts in Turbulent Combustion,” Proc. Combust. Inst., 21, pp. 1231–1250) represents the turbulent flame brush using statistical averaging of laminar flamelets whose structure is not affected by turbulence. The chemical nonequilibrium effects considered in this model are due to local turbulent straining only. In contrast, the flamelet-generated manifold (FGM) (van Oijen and de Goey, 2000, “Modeling of Premixed Laminar Flames Using Flamelet-Generated Manifolds,” Combust. Sci. Technol., 161, pp. 113–137) model considers that the scalar evolution; the realized trajectories on the thermochemical manifold in a turbulent flame are approximated by the scalar evolution similar to that in a laminar flame. This model does not involve any assumption on flame structure. Therefore, it can be successfully used to model ignition, slow chemistry, and quenching effects far away from the equilibrium. In FGM, 1D premixed flamelets are solved in reaction-progress space rather than physical space. This helps better solution convergence for the flamelets over the entire mixture fraction range, especially with large kinetic mechanisms at the flammability limits (ANSYS FLUENT 14.5 Theory Guide Help Document, http://www.ansys.com). In the present work, a systematic comparative study of the FGM model with the LFM for four different turbulent diffusion/premixed flames is presented. The first flame considered in this work is methane-air flame with dilution air at the downstream. The second and third flames considered are jet flames in a coaxial flow of hot combustion products from a lean premixed flame called Cabra lifted H2 and CH4 flames (Cabra, et al., 2002, “Simultaneous Laser Raman-Rayleigh-LIF Measurements and Numerical Modeling Results of a Lifted Turbulent H2/N2 Jet Flame in a Vitiated Coflow,” Proc. Combust. Inst., 29(2), pp. 1881–1888; Lifted CH4/Air Jet Flame in a Vitiated Coflow, http://www.me.berkeley.edu/cal/vcb/data/VCMAData.html) where the reacting flow associated with the central jet exhibits similar chemical kinetics, heat transfer, and molecular transport as recirculation burners without the complex recirculating fluid mechanics. The fourth flame considered is a Sandia flame D (Barlow et al., 2005, “Piloted Methane/Air Jet Flames: Scalar Structure and Transport Effects,” Combust. Flame, 143, pp. 433–449), a piloted methane-air jet flame. It is observed that the simulation results predicted by the FGM model are more physical and accurate compared to the LFM in all the flames presented in this work. The autoignition-controlled flame lift-off is also captured well in the cases of lifted flames using the FGM model.

Efficient turbulent combustion models are typically designed for the numerical simulation of two-stream problems, namely, the combustion of fuel in air. There are applications, however, where large amounts of a diluent such as water steam or recirculated exhaust gas is supplied to the combustor independent of fuel and air supplies. In such cases, classical approaches become quite time-consuming. In the present paper, a new three-stream flamelet model is presented, which is essentially an extension of the two-stream flamelet model for diffusion flames. Key points of the approach are the introduction of a second mixture fraction variable and the efficient establishment of the flamelet library. After presentation of the theory, the applicability of the new model is demonstrated by comparison with experimental results for the lift-off height of jet diffusion flames.

A rational basis for correlating turbulent burning velocities is shown to involve the product of the Karlovitz stretch factor and the Lewis number. A generalized expression is derived to show how flame stretch is related to the velocity field. A new dimensionless correlation of experimental values of turbulent burning velocities is presented. Dimensionless groups also are used in correlations of laminar and turbulent flame extinction stretch rates. A distribution function of stretch rates in turbulent flames, based on an earlier one of Yeung et al ., is proposed and the experimental data are well predicted by a theory based on flamelet extinction by flame stretch with this distribution. Uncertainties arise concerning the role of negative stretch rate. Laminar flamelet modelling of complex combustion appears to have a broader validity than might be expected and some explanation for this is offered.

A laminar flamelet model of pre-mixed turbulent combustion is described in which a characteristic length scale L̂ y controls the flamelet surface-to-volume ratio. An analysis, based on the Bray-Moss-Libby model of turbulent combustion, leads to the conclusion that L̂ y /l is proportional to the ratio of the laminar burning velocity to the turbulence velocity u' , where l is the integral length scale of the turbulence. A fractal flame model and an analysis of experimental time series data both support this conclusion. Several different theories for the turbulent burning velocity are shown to be equivalent to each other and to be generalizations of the classical theory of Kolmogorov, Petrovski & Piskonov. A method of characteristics analysis confirms the resulting expression. This expression, containing only one disposable constant which must be of order unity, is compared with a published correlation of a large amount of experimental data. This leads to an experimental determination of the ratio of effective to true laminar burning velocities, as a function of Karlovitz number, which shows satisfactory agreement with results of strained laminar flame calculations.

Abstract A counterflow diffusion flame for supercritical CO2 combustion is investigated at various CO2 dilution levels and pressures by accounting for real gas effects into both thermal and transport properties. The UCF 1.1 24-species mechanism is used to account the chemistry. The nature of important nonpremixed combustion characteristics such as Prandtl number, thermal diffusivity, Lewis number, stoichiometric scalar dissipation rate, flame thickness, and Damköhler number are investigated with respect to CO2 dilution and pressure. The results show that the aforementioned parameters are influenced by both dilution and pressure; the dilution effect is more dominant. Further, the result shows that Prandtl number increases with CO2 dilution and at 90% CO2 dilution, the difference between the Prandtl number of the inlet jets and the flame is minimal. Also, the common assumption of unity Lewis number in the theory and modeling of nonpremixed combustion does not hold reasonable for sCO2 applications due to large difference of Lewis number across the flame and the Lewis number on the flame drop significantly with an increase in the CO2 dilution. An interesting relation between Lewis number and CO2 dilution is observed. The Lewis number of species drops by 15% when increasing the CO2 dilution by 30%. Increasing the CO2 dilution increases both the flow and chemical timescales; however, chemical timescale increases faster than the flow timescales. The magnitudes of the Damköhler number signify the need to consider finite rate chemistry for sCO2 applications. Further, the Damköhler numbers at 90% sCO2 dilution are very small; hence, laminar flamelet assumptions in turbulent combustion simulations are not physically correct for this application. Also, it is observed that the Damköhler number drops nonlinearly with increasing CO2 dilution in the oxidizer stream. This is a very important observation for the operation of sCO2 combustors. Further, the flame thickness is found to increase with CO2 dilution and reduce with pressure.

International audience In an effort to continue the pioneering work of Harary in USA and Flament in France, we have undertaken to develop, on an experimental basis, a formalized theory of systems of beliefs and their modifications. This theory uses the psycho-social concepts of theories of cognitive consistency and of the tools of discrete mathematics, such as rewriting and intervals within graphs. The axioms and rewriting rules are elaborated from experimental data, and we demonstrate that the system we have built has the property of termination. This result is in accordance with experimental observations that show that every subject having an inconsistent system of beliefs (i.e., one containing contradictions) makes this system evolve towards consistency to reach a simple, consistent reference framework.

Elizabeth Wilmot, Countess of Rochester, is best known to most modern readers as the woman John Wilmot, Earl of Rochester, abducted and later wed. As Samuel Pepys memorably records in his diary entry for 28 May 1665:Thence to my Lady Sandwich’s, where, to my shame, I had not been a great while before. Here, upon my telling her a story of my Lord Rochester’s running away on Friday night last with Mrs Mallet, the great beauty and fortune of the North, who had supped at Whitehall with Mrs Stewart, and was going home to her lodgings with her grandfather, my Lord Haly, by coach; and was at Charing Cross seized on by both horse and footmen, and forcibly taken from him, and put into a coach with six horses, and two women provided to receive her, and carried away. Upon immediate pursuit, my Lord of Rochester (for whom the King had spoke to the lady often, but with no success) was taken at Uxbridge; but the lady is not yet heard of, and the King mighty angry and the Lord sent to the Tower. (http://www.pepysdiary.com/)Here Pepys provides an anecdote that offers what Helen Deutsch has described in another context as “the elusive possibility of truth embodied by ‘things in themselves,’ by the things, that is, preserved in anecdotal form” (28). Pepys’s diary entry yields up an “elusive possibility” of embodied truth; his version of Wilmot’s abduction solidifies what he perceives to be the most notable features of her identity: her beauty, her wealth, and her sexual trajectory.Pepys’s conclusion that “the lady is not yet heard of” complicates this idea of anecdotal preservation, for he neatly ties up his story of Wilmot’s body by erasing her from it: she is removed, voiceless and disembodied, from even this anecdote of her own abduction. Pepys’s double maneuver demonstrates the complex set of interactions surrounding the preservation of early modern women’s sexual and textual selves. Written into Pepys’s diary and writing in conversation with her husband, Wilmot has generally been treated as a subordinate historical and literary figure—a character rather than an agent or an author. The richness of Wilmot’s own writing has been largely ignored; her manuscript poetry has been treated as an artefact and a source of autobiographical material, whereas Rochester’s poetry—itself teeming with autobiographical details, references to material culture, and ephemera—is recognised and esteemed as literary. Rochester’s work provides a tremendous resource, a window through which we can read and re-read his wife’s work in ways that enlighten and open up readings rather than closing them down, and her works similarly complicate his writings.By looking at Wilmot as a case study, I would like to draw attention to some of the continued dilemmas that scholars face when we attempt to recover early modern women’s writing. With this study, I will focus on distinct features of Wilmot’s sexual and textual identity. I will consider assumptions about female docility; the politics and poetics of erotic espionage; and Wilmot’s construction of fugitive desires in her poetry. Like the writings of many early modern women, Wilmot’s manuscript poetry challenges assumptions about the intersections of gender, sexuality, and authorship. Early Modern Women’s Docile Bodies?As the entry from Pepys’s diary suggests, Wilmot has been constructed as a docile female body—she is rendered “ideal” according to a set of gendered practices by which “inferior status has been inscribed” on her body (Bartky 139). Contrasting Pepys’s references to Wilmot’s beauty and marriageability with Wilmot’s own vivid descriptions of sexual desire highlights Wilmot’s tactical awareness and deployment of her inscribed form. In one of her manuscript poems, she writes:Nothing ades to Loves fond fireMore than scorn and cold disdainI to cherish your desirekindness used but twas in vainyou insulted on your SlaveTo be mine you soon refusedHope hope not then the power to haveWhich ingloriously you used. (230)This poem yields up a wealth of autobiographical information and provides glimpses into Wilmot’s psychology. Rochester spent much of his married life having affairs with women and men, and Wilmot represents herself as embodying her devotion to her husband even as he rejects her. In a recent blog entry about Wilmot’s poetry, Ellen Moody suggests that Wilmot “must maintain her invulnerable guard or will be hurt; the mores damn her whatever she does.” Interpretations of Wilmot’s verse typically overlay such sentiments on her words: she is damned by social mores, forced to configure her body and desire according to rigorous social codes that expect women to be pure and inviolable yet also accessible to their lovers and “invulnerable” to the pain produced by infidelity. Such interpretations, however, deny Wilmot the textual and sexual agency accorded to Rochester, begging the question of whether or not we have moved beyond reading women’s writing as essential, natural, and embodied. Thus while these lines might in fact yield up insights into Wilmot’s psychosocial and sexual identities, we continue to marginalise her writing and by extension her author-self if we insist on taking her words at face value. Compare, for example, Wilmot’s verse to the following song by her contemporary Aphra Behn:Love in Fantastique Triumph satt,Whilst Bleeding Hearts a round him flow’d,For whom Fresh paines he did Create,And strange Tyranick power he show’d;From thy Bright Eyes he took his fire,Which round about, in sports he hurl’d;But ’twas from mine, he took desire,Enough to undo the Amorous World. (53) This poem, which first appeared in Behn’s tragedy Abdelazer (1677) and was later printed in Poems upon Several Occasions (1684), was one of Behn’s most popular lyric verses. In the 1920s and 1930s Ernest Bernbaum, Montague Summers, Edmund Gosse, and others mined Behn’s works for autobiographical details and suggested that such historical details were all that her works offered—a trend that continued, disturbingly, into the later half of the twentieth century. Since the 1980s, Paula R. Backscheider, Ros Ballaster, Catherine Gallagher, Robert Markley, Paul Salzman, Jane Spencer, and Janet Todd have shown that Behn’s works are not simple autobiographical documents; they are the carefully crafted productions of a literary professional. Even though Behn’s song evokes a masochistic relationship between lover and beloved much like Wilmot’s song, critics treat “Love Arm’d” as a literary work rather than a literal transcription of female desire. Of course there are material differences between Wilmot’s song and Behn’s “Love Arm’d,” the most notable of which involves Behn’s self-conscious professionalism and her poem’s entrenchment in the structures of performance and print culture. But as scholars including Kathryn King and Margaret J. M. Ezell have begun to suggest, print publication was not the only way for writers to produce and circulate literary texts. King has demonstrated the ways in which female authors of manuscripts were producing social texts (563), and Ezell has shown that “collapsing ‘public’ into ‘publication’” leads modern readers to “overlook the importance of the social function of literature for women as well as men” (39). Wilmot’s poems did not go through the same material, ideological, and commercial processes as Behn’s poems did, but they participated in a social and cultural network of exchange that operated according to its own rules and that, significantly, was the same network that Rochester himself used for the circulation of his verses. Wilmot’s writings constitute about half of the manuscript Portland PwV 31, held by Hallward Library, University of Nottingham—a manuscript catalogued in the Perdita Project but lacking a description and biographical note. Teresa D. Kemp has discussed the impact of the Perdita Project on the study of early modern women’s writing in Feminist Teacher, and Jill Seal Millman and Elizabeth Clarke (both of whom are involved with the project) have also written articles about the usability of the database. Like many of the women writers catalogued by the Perdita Project, Wilmot lacks her own entry in the Dictionary of National Biography and is instead relegated to the periphery in Rochester’s entry.The nineteen-page folio includes poems by both Rochester and Wilmot. The first eight poems are autograph manuscript poems by Rochester, and a scene from a manuscript play ‘Scaene 1st, Mr. Daynty’s chamber’ is also included. The remaining poems, excluding one without attribution, are by Wilmot and are identified on the finding aid as follows:Autograph MS poem, entitled ‘Song’, by Elizabeth WilmotAutograph MS poem, entitled ‘Song’, by Elizabeth WilmotAutograph MS poem, entitled ‘Song’, by Elizabeth WilmotMS poem, untitled, not ascribed Autograph MS poem, entitled ‘Song’, by Elizabeth WilmotAutograph MS poem, untitled, by Elizabeth WilmotAutograph MS poem, untitled, by Elizabeth WilmotAutograph MS poem, untitled, by Elizabeth Wilmot Autograph MS poem, untitled, by Elizabeth WilmotTwo of the songs (including the lyric quoted above) have been published in Kissing the Rod with the disclaimer that marks of revision reveal that “Lady Rochester was not serving as an amanuensis for her husband” yet the editors maintain that “some sort of literary collaboration cannot be ruled out” (230), implying that Rochester helped his wife write her poetry. Establishing a non-hierarchical strategy for reading women’s collaborative manuscript writing here seems necessary. Unlike Behn, who produced works in manuscript and in print and whose maximization of the slippages between these modes has recently been analyzed by Anne Russell, Wilmot and Rochester both wrote primarily in manuscript. Yet only Rochester’s writings have been accorded literary status by historians of the book and of manuscript theory such as Harold Love and Arthur Marotti. Even though John Wilders notes that Rochester’s earliest poems were dialogues written with his wife, the literariness of her contributions is often undercut. Wilders offers a helpful suggestion that the dialogues set up by these poems helps “hint … at further complexities in the other” (51), but the complexities are identified as sexual rather than textual. Further, the poems are treated as responses to Rochester rather than conversations with him. Readers like Moody, moreover, draw reflections of marital psychology from Wilmot’s poems instead of considering their polysemic qualities and other literary traits. Instead of approaching the lines quoted above from Wilmot’s song as indications of her erotic and conjugal desire for her husband, we can consider her confident deployment of metaphysical conceits, her careful rhymes, and her visceral imagery. Furthermore, we can locate ways in which Wilmot and Rochester use the device of the answer poem to build a complex dialogue rather than a hierarchical relationship in which one voice dominates the other. The poems comprising Portland PwV 31 are written in two hands and two voices; they complement one another, but neither contains or controls the other. Despite the fact that David Farley-Hills dismissively calls this an “‘answer’ to this poem written in Lady Rochester’s handwriting” (29), the verses coexist in playful exchange textually as well as sexually. Erotic Exchange, Erotic EspionageBut does a reorientation of literary criticism away from Wilmot’s body and towards her body of verse necessarily entail a loss of her sexual and artefactual identity? Along with the account from Pepys’s diary mentioned at the outset of this study, letters from Rochester to his wife survive that provide a prosaic account of the couple’s married life. For instance, Rochester writes to her: “I love not myself as much as you do” (quoted in Green 159). Letters from Rochester to his wife typically showcase his playfulness, wit, and ribaldry (in one letter, he berates the artist responsible for two miniatures of Wilmot in strokes that are humorous yet also charged with a satire that borders on invective). The couple’s relationship was beleaguered by the doubts, infidelities, and sexual double standards that an autobiographical reading of Wilmot’s songs yields up, therefore it seems as counterproductive for feminist literary theory, criticism, and recovery work to entirely dispense with the autobiographical readings as it seems reductive to entirely rely on them. When approaching works like these manuscript poems, then, I propose using a model of erotic exchange and erotic espionage in tandem with more text-bound modes of literary criticism. To make this maneuver, we might begin by considering Gayle Rubin’s proposition that “If women are the gifts, then it is men who are the exchange partners. And it is the partners, not the presents, upon whom reciprocal exchange confers its quasi-mystical power of social linkage” (398). Wilmot’s poetry relentlessly unsettles the binary set up between partner and present, thereby demanding a more pluralistic identification of sexual and textual economies. Wilmot constructs Rochester as absent (“Thats caused by absence norished by despaire”), which is an explicit inversion of the gendered terms stereotypically deployed in poetry (the absent woman in works by Rochester as well as later satirists like Jonathan Swift and Alexander Pope often catalyzes sexual desire) that also registers Wilmot’s autobiographical contexts. She was, during most of her married life, living with his mother, her own mother, and Rochester’s nieces in his house at Adderbury while he stayed in London. The desire in Wilmot’s poetry is textualised as much as it is sexualised; weaving this doublebraid of desires and designs together ultimately provides the most complete interpretation of the verses. I read the verses as offering a literary form of erotic espionage in which Wilmot serves simultaneously as erotic object and author. That is, she both is and is not the Cloris of her (and Rochester’s) poetry, capable of looking on and authorizing her desired and desiring body. The lyric in which Wilmot writes “He would return the fugitive with Shame” provides the clearest example of the interpretive tactic that I am proposing. The line, from Wilmot’s song “Cloris misfortunes that can be exprest,” refers to the deity of Love in its complete context:Such conquering charmes contribute to my chainAnd ade fresh torments to my lingering painThat could blind Love juge of my faithful flameHe would return the fugitive with ShameFor having bin insenceable to loveThat does by constancy it merritt prove. (232)The speaker of the poem invokes Cupid and calls on “blind Love” to judge “my faithful flame.” The beloved would then be returned “fugitive with Shame” because “blind Love” would have weighed the lover’s passion and the beloved’s insensibility. Interestingly, the gender of the beloved and the lover are not marked in this poem. Only Cupid is marked as male. Although the lover is hypothetically associated with femaleness in the final stanza (“She that calls not reason to her aid / Deserves the punishmentt”), the ascription could as easily be gendering the trait of irrationality as gendering the subject/author of the poem. Desire, complaint, and power circulate in the song in a manner that lacks clear reference; the reader receives glimpses into an erotic world that is far more ornately literary than it is material. That is, reading the poem makes one aware of tropes of power and desire, whereas actual bodies recede into the margins of the text—identifiable because of the author’s handwriting, not a uniquely female perspective on sexuality or (contrary to Moody’s interpretation) a specifically feminine acquiescence to gender norms. Strategies for Reading a Body of VerseWilmot’s poetry participates in what might be described as two distinct poetic and political modes. On one hand, her writing reproduces textual expectations about Restoration answer poems, songs and lyrics, and romantic verses. She crafts poetry that corresponds to the same textual conventions that men like Rochester, John Dryden, Abraham Cowley, and William Cavendish utilised when they wrote in manuscript. For Wilmot, as for her male contemporaries, such manuscript writing would have been socially circulated; at the same time, the manuscript documents had a fluidity that was less common in print texts. Dryden and Behn’s published writings, for instance, often had a more literary context (“Love Arm’d” refers to Abdelazer, not to Behn’s sexual identity), whereas manuscript writing often referred to coteries of readers and writers, friends and lovers.As part of the volatile world of manuscript writing, Wilmot’s poetry also highlights her embodied erotic relationships. But over-reading—or only reading—the poetry as depicting a conjugal erotics limits our ability to recover Wilmot as an author and an agent. Feminist recovery work has opened many new tactics for incorporating women’s writing into existing literary canons; it has also helped us imagine ways of including female domestic work, sexuality, and other embodied forms into our understanding of early modern culture. By drawing together literary recovery work with a more material interest in recuperating women’s sexual bodies, we should begin to recuperate women like Wilmot not simply as authors or bodies but as both. 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