Andrea Bucchi

Transpiration Cooling Performance in LOX/Methane Liquid-Fuel Rocket Engines

A transpiration cooling model using high-pressure, real gas properties has been developed in order to determine methane transpiration cooling performance in the throat region of a high thrust,high-pressure LOX/LCH4 liquid rocket engine (LRE), such as those being currently investigated in European Union (EU). The model is a series of non linear ordinary differential equations one-dimensional for the conduction-convection of heat between the coolant and the porous material and neglects for simplicity vapour formation. This last assumption occurs, in fact, only with low thermal conductivity materials (kwall = 20 W/mK) and at low cool antinjection temperature (Tcool_in = 140 K), these conditions being present only in 3 of the 21cases examined in the parametric analysis. Only steady-state results are presented;comparisons were not made to test data as experiments to this purpose are still in the planning process. Temperature profiles along the liner wall have been numerically obtained by varying liner porosity (e = 15% ÷17%), conductivity (kwall = 20 W/mK and 100 W/mK) and coolant injection temperature (Tcool-in = 140 and 300 K). Results indicate that profiles of temperatures,pressure and density tend to have sharp gradients near the hot gas porous wall interface. They also show that very low surface temperatures (Tmax = 500, 600 and 700 K) are possible with a methane transpiration flow rate corresponding to about 5 percent, or less, of that injected in the combustion chamber. The associated specific impulse loss due to the coolant flow rate injected may be at least partially recovered by the increase of turbo-pump efficiency, since pressure losses in the cooling circuit are substantially reduced; furthermore, based on wall temperature predicted, reusability appears potentially higher than that obtainable with other regenerative cooling systems.

Investigation of transpiration cooling performance in lox/methane liquid rocket engines

A transpiration cooling model using high-pressure, real gas properties has been developed in order to determine methane transpiration cooling performance in the throat region of a high thrust,high-pressure LOX/LCH4 liquid rocket engine (LRE), such as those being currently investigated in European Union (EU). The model is a series of non linear ordinary differential equations one-dimensional for the conduction-convection of heat between the coolant and the porous material and neglects for simplicity vapour formation. This last assumption occurs, in fact, only with low thermal conductivity materials (kwall = 20 W/mK) and at low cool antinjection temperature (Tcool_in = 140 K), these conditions being present only in 3 of the 21cases examined in the parametric analysis. Only steady-state results are presented;comparisons were not made to test data as experiments to this purpose are still in the planning process. Temperature profiles along the liner wall have been numerically obtained by varying liner porosity (e = 15% ÷17%), conductivity (kwall = 20 W/mK and 100 W/mK) and coolant injection temperature (Tcool-in = 140 and 300 K). Results indicate that profiles of temperatures,pressure and density tend to have sharp gradients near the hot gas porous wall interface. They also show that very low surface temperatures (Tmax = 500, 600 and 700 K) are possible with a methane transpiration flow rate corresponding to about 5 percent, or less, of that injected in the combustion chamber. The associated specific impulse loss due to the coolant flow rate injected may be at least partially recovered by the increase of turbo-pump efficiency, since pressure losses in the cooling circuit are substantially reduced; furthermore, based on wall temperature predicted, reusability appears potentially higher than that obtainable with other regenerative cooling systems.

A transverse isotropic viscoelastic constitutive model for aortic valve tissue

A new anisotropic viscoelastic model is developed for application to the aortic valve (AV). The directional dependency in the mechanical properties of the valve, arising from the predominantly circumferential alignment of collagen fibres, is accounted for in the form of transverse isotropy. The rate dependency of the valves mechanical behaviour is considered to stem from the viscous (η) dissipative effects of the AV matrix, and is incorporated as an explicit function of the deformation rate (λ˙). Model (material) parameters were determined from uniaxial tensile deformation tests of porcine AV specimens at various deformation rates, by fitting the model to each experimental dataset. It is shown that the model provides an excellent fit to the experimental data across all different rates and satisfies the condition of strict local convexity. Based on the fitting results, a nonlinear relationship between η and λ˙ is established, highlighting a ‘shear-thinning’ behaviour for the AV with increase in the deformation rate. Using the model and these outcomes, the stress–deformation curves of the AV tissue under physiological deformation rates in both the circumferential and radial directions are predicted and presented. To verify the predictive capabilities of the model, the stress–deformation curves of AV specimens at an intermediate deformation rate were estimated and validated against the experimental data at that rate, showing an excellent agreement. While the model is primarily developed for application to the AV, it may be applied without the loss of generality to other collagenous soft tissues possessing a similar structure, with a single preferred direction of embedded collagen fibres.

The role of pre-conditioning frequency in the experimental characterisation of hyper-elastic materials as models for soft tissue applications

Rubber-like materials as many soft tissues can be described as incompressible and hyper-elastic materials. Their comparable elastic behavior, up to a certain extent, has been exploited to develop and test experimental methodologies to be then applied to soft biological tissues such as aortic wall. Hence, theoretical and experimental simulation of aortic tissue, and more generally blood vessel tissue, has been often conducted using rubbers. Despite all the efforts in characterizing such materials, a clear and comprehensive testing procedure is still missing. In particular, the influence of pre-conditioning in the mechanical response of hyper-elastic materials has been often neglected. In this paper, the importance of pre-conditioning is demonstrated by: (i) exploring the effect of stretching frequency applied before the uniaxial tensile test; (ii) recognizing the role of specimen geometry and strain amplitude; (iii) verifying the impact of experimental data acquisition on finite element predictions. It was found that stress–strain relationship shows a statistical difference between some frequencies of pre-conditioning and its absence. Only certain pre-conditioning frequencies were able to generate repeatable experimental data for strip or dumb-bell shapes. This feature corresponds to a consistent reduction in the scatter of critical pressures obtained by numerical simulations.

Unified viscoelasticity: applying discrete element models to soft tissues with two characteristic times

Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues.

The effect of thickness measurement on numerical arterial models

Several optical-based techniques for measuring the sample thickness (ST) of soft tissues have been proposed in the literature to overcome the limits of hand-operated procedures. However, ST measurement still remains arbitrary. The stress calculated during an experimental procedure, usually based on a constant thickness value for all samples, cannot be considered representative of the actual stress experienced by the tissue. Therefore, a new optical methodology to measure ST is proposed and compared to four different thickness estimations. A simplified aortic geometry, under physiologic pulsatile conditions, is used to assess the impact of ST measurement on stress predictions. An additional computational model investigates the effect of such thickness values on critical pressure levels that may instigate aneurysm formation in a homogeneous or artificially modified geometry. Comparing the results obtained for the application of a pulsatile load, wall stress values associated to minimum ST are at least 24kPa inferior to maximum ST. Critical pressure values appear to be inversely proportional to ST estimation: simulations, associated to maximum ST, predict aneurysm formation for pressure levels at least 7kPa inferior to minimum ST outcomes. Finally, the role of the strain-energy function used to fit the experimental data is demonstrated to be fundamental for predictions of aneurysm formation.

A transverse isotropic constitutive model for the aortic valve tissue incorporating rate-dependency and fibre dispersion: Application to biaxial deformation

This paper presents a continuum-based transverse isotropic model incorporating rate-dependency and fibre dispersion, applied to the planar biaxial deformation of aortic valve (AV) specimens under various stretch rates. The rate dependency of the mechanical behaviour of the AV tissue under biaxial deformation, the (pseudo-) invariants of the right Cauchy-Green deformation-rate tensor Ċ associated with fibre dispersion, and a new fibre orientation density function motivated by fibre kinematics are presented for the first time. It is shown that the model captures the experimentally observed deformation of the specimens, and characterises a shear-thinning behaviour associated with the dissipative (viscous) kinematics of the matrix and the fibres. The application of the model for predicting the deformation behaviour of the AV under physiological rates is illustrated and an example of the predicted σ-λ curves is presented. While the development of the model was principally motivated by the AV biomechanics requisites, the comprehensive theoretical approach employed in the study renders the model suitable for application to other fibrous soft tissues that possess similar rate-dependent and structural attributes.