Pressure Distribution Characteristics Research Articles

Experimental study of solid circulation rate and pressure distribution characteristics in a cold fluidized bed with an external heat exchanger in an municipal solid waste incinerator

AbstractThe external heat exchanger (EHE) can solve the problem of the insufficient heating surface due to the large‐scale circulating fluidized bed (CFB) boiler effectively; furnace temperature and bed temperature can be regulated quickly and accurately with the adjustment of the solids circulation rate (SCR). The ash differs from coal‐fired boilers in particle size, density, and other physical parameters, so the circulation and heat transfer characteristics are not identical. The results of SCR and pressure distribution in a cold CFB experimental system with an EHE in which the height of the partition (HP) could be adjusted were analyzed. Experiments studied the effect of fluidized air velocity in the riser (Ug), HP of the EHE, and the pressure of the supply air chamber (PSA) in the EHE on SCR using quartz sand with an average size of 0.239 mm. It was noted that SCR increased with Ug and PSA in the range of 7.01–28.37 g/s with the increase in Ug, and the maximum value of SCR was obtained when PSA was 750 Pa and the HP was 80 mm. The experiments also noted that the increase in SCR significantly affected the pressure distribution in the region of high solids content (EHE and the region above 600 mm in the riser). A reference to the above characteristics of SCR and pressure distribution variations can be considered for operating commercial CFB waste incinerators.

Experimental and numerical investigation on the wake flow and vortex shedding of a rotating circular cylinder

When fluid passes through a still cylinder, alternate shedding vortices are formed on the two sides of the cylinder in the wake. Regarding a rotating circular cylinder, the rotation can affect the wake flow and vortex shedding pattern. To investigate the wake flow and surface pressure characteristics of a rotating cylinder at different rotational speeds, wind tunnel tests and numerical simulation methods through Fluent were used. The dimensionless rotational speed was discussed for its impact on the vortex shedding intensity and pattern. Additionally, the correlation between the cylinder surface wind pressure and the vortex shedding pattern was analyzed. The results of this study provide useful insights into the mechanisms underlying the vortex shedding phenomenon and the effects of rotational speed on the wake flow and surface pressure of a rotating cylinder. The results show that an increase in the dimensionless rotational speed will change the characteristics of the wind pressure distribution, leading to the variation in aerodynamic coefficients. On the other hand, the vortex shedding characteristics of the wake flow will also be affected, with changes in the vortex shedding pattern and direction, thereby changing the characteristics of the wake deviation angle and correlation. Based on the analysis of wake flow speed power spectrum characteristics and the Reynolds number effect, the mechanism of the vortex shedding change caused by flow transitions is speculated and verified by numerical simulation of the vorticity field.

Numerical study of the influence of blade inlet design parameters on the internal flow characteristics and energy performance of a Francis turbine

One of the challenges of hydraulic turbine design is the creation of a conveyor with high hydraulic performance in accordance with the parameters of the hydraulic energy. The blade inlet parameters, such as blade beta angle, lean angle, and ellipse axis ratio, have an effect on the performance and cavitation characteristics of the runner, among the numerous geometric elements that regulate turbine performance. All of these parameters must be optimized to ensure that the runner inlet is matched to the guide vane under design conditions and a wider range of off-design conditions. For hydraulic designers, computational fluid dynamics based performance prediction methods can provide rapid turbine performance predictions and expedite runner development. Finding a collection of accessible parameters, meanwhile, strongly depends on the designer’s previous design work, which is frequently time-consuming. In this article, the internal flow characteristics and energy performance of a Francis turbine with moderate specific-speed, as well as the blade leading edge geometrical parameters that influence them, are investigated in depth. The Francis turbine is designed in accordance with the rated head H (m), rated flow rate Q (m), and rated speed n (rpm) within the constraints of the fixed meridional projection, including the leading-edge and trailing-edge positions. The energy performance, internal flow characteristics, velocity profile, flow angles, pressure distribution, blade loading, and cavitation characteristics are computed, analyzed, and compared. The main findings can serve as a guide for the development of Francis turbines with moderate specific-speed.

Aerodynamic analysis of an ultra–long and ultra–wide industrial building under wind loading: Insights into flow dynamics and pressure distribution characteristics

Large ultra–long and ultra–wide industrial facilities have a huge windward surface, resulting in severe wind suction on the roof, back, and side enclosures. Wind–induced damage on structures may occur due to the turbulence effect caused by airflow over the irregular shape of the roof, which results in complex wind pressure distribution characteristics on the roof. Therefore, it is critical to elucidate the pressure distribution of ultra–long and ultra–wide structures to ensure the normal functioning of the structure and predict wind–induced dynamic disasters. In this paper, the wind–induced pressure field characteristics of ultra–long and ultra–wide roof structures are investigated by Computational Fluid Dynamics (CFD) analysis. A series of qualitative and quantitative analyses were performed to assess the pressure coefficient distribution on the roof as a result of wind direction angle, terrain roughness, and size effect. Meanwhile, the complicated variations in the wind field of the structure generated by the flow around bluff bodies are studied to establish a relationship between flow dynamics and pressure distribution characteristics. The results showed that the roof is mainly exposed to wind suction under the influence of wind attack angle, and the region with severe negative pressure gradient change is controlled by the large–scale eddies generated from the separated airflow. Moreover, the terrain roughness and size effect intricately modify the pressure distribution pattern on the local roof, and wind pressure intensity may be estimated using the information on eddy diffusion and velocity distribution.

Comparison of the plantar pressure distribution and mechanical alignment in patients with varus knee osteoarthritis following high tibial osteotomy

PurposeThe changes in the lower limb alignment were vitally important after high tibial osteotomy (HTO). Therefore, the purpose of present study was to analyze the characteristics of plantar pressure distribution after HTO, and to investigate the effect of plantar pressure distribution on postoperative limb alignment.MethodsBetween May 2020 and April 2021, varus knee patients undergoing HTO were evaluated in the present study. The peak pressure of plantar regions, medial-lateral pressure ratio (MLPR), foot progression angle (FTA), anteroposterior COP (AP-COP), lateral symmetry of COP (LS-COP), and the radiographic parameters were evaluated preoperatively and at the final follow-up. Compared among the slight valgus (SV), moderate valgus (MV) and large valgus (LV) groups at the final follow-up, the peak pressure of HM, HC and M5 regions, and the MLPR were compared; the Knee Injury and Osteoarthritis Outcome Score4 (KOOS4) including four subscales, and the American of orthopedic foot and ankle society (AOFAS) were evaluated.ResultsThe WBL%, HKA and TPI angle changed significantly after HTO (P < 0.001). The preoperative group exhibited a lower peak pressure in the HM region (P < 0.05) and higher peak pressure in the M5 region (P < 0.05); the pre- and postoperative groups exhibited a lower peak pressure in the HC region (P < 0.05); the rearfoot MLPR was significantly lower and LS-COP was significantly higher in the preoperative group (P = 0.017 in MLPR and 0.031 in LS-COP, respectively). Comparison among the SV, MV and LV groups, the SV group indicated a lower peak pressure in the HM region (P = 0.036), and a lower MLPR in the rearfoot (P = 0.033). The KOOS Sport/Re score in the MV and LV groups increased significantly compared with the SV group (P = 0.042).ConclusionPlantar pressure distribution during the stance phase in patients with varus knee OA following HTO exhibited a more medialized rearfoot plantar pressure distribution pattern than that before surgery. Compared with the small valgus alignment, a moderate to large valgus alignment allows patients to walk with a more even medial and lateral plantar pressure distribution, which is more similar to healthy adults.

Numerical analysis method for intra-stage non-equilibrium two-phase condensing flow in wet steam turbine and its application

To improve the numerical calculation performance of the intra-stage wet steam non-equilibrium condensing flow in a wet steam turbine, this paper proposed a numerically modified wet steam non-equilibrium condensation (NEC) model by considering the interphase heat and mass transfer in the Euler/Euler coordinate system. The model was developed based on nucleation kinetics, and the expressions of the critical droplet formation free energy and the nucleation rate were given. First, combining the experimental data, the non-isothermal effect nucleation model was modified by the surface tension coefficient method. Then, the low-pressure modified droplet growth model, which is suitable for describing any range of Knudsen numbers, was employed to calculate the droplet surface heat and mass transfer process, and the steam/liquid two-phase control equations and the turbulence model were presented. Meanwhile, the parameter transfer and coupling problem between the vapor and liquid phases was solved. Subsequently, the modified model and the original model were adopted to solve the wet steam condensing flow at the 1D Moses-Stein nozzle numerically, and the results showed that the modified model could calculate the distribution characteristics of pressure and droplet radius more accurately and fit the experimental results better. Afterward, the characteristicsof the non-equilibrium condensing flow of wet steam in the steam turbine cascade were investigated. Finally, combined with the experimental result on the pressure distribution in the steam turbine plane static cascade, the validity of the proposed numerically modified model was further verified, which provided a theoretical basis for the high-accuracy numerical analysis of the condensing flow in the nuclear power wet steam turbine cascade.

Experiment and instantaneous driving simulation of explosion dispersion process of central tube for submunition

In order to study the influence of explosion dispersion of submunition on the dispersion velocity and pressure characteristics of subunits, the experimental study of explosive dispersion of the central tube was carried out when the explosives with low detonation velocity were applied in central tube as the main charge. In addition, the explosion dispersion test process was recorded by high-speed photography. RDX-based aluminized explosive samples with low detonation velocity were prepared and tested, and the low detonation velocity performance changes under different charge diameters and densities were obtained. Based on the explosive dispersion test of the central tube of the submunition, the physical model and three-dimensional axisymmetric finite element model of the central tube, subunit and aluminium alloy shell with prefabricated grooves are established. The fluid-structure coupling calculation method is used to simulate the explosive dispersion process. The simulation results are compared with the test results, and the pressure distribution characteristics of the subunit and the variation law of the dispersion velocity are analyzed. The effectiveness of the engineering calculation method of JWL equation model parameters is verified. The results show that using RDX based aluminized low detonation velocity explosive as the main charge of the central tube structure can achieve the design goal of the explosive dispersion for submunition, and the explosion dispersion model of submunition can accurately describe the dispersion characteristics of the subunit. The research results can be used to guide the structural design of submunition warhead.

Experimental Study on the Preparation of Hydrogen-Rich Gas by Gasifying of Traditional Chinese Medicine Residue in a DFB Based on Calcium Looping

Using traditional Chinese medicine residue biomass as the raw material and industrial limestone as a carbon absorbent, this paper investigates the production of hydrogen-rich synthesis gas in a pilot-scale calcium looping dual fluidized bed (DFB) system. The study focuses on analyzing the distribution characteristics of temperature and pressure, as well as the operation and control methods of the DFB system. The effects of reaction temperature, material layer height (residence time), water vapor/biomass ratio (S/B), and calcium/carbon molar ratio (Ca/C) on gasification products are examined. The experimental results demonstrate that as the temperature (600–700 °C), S/B ratio (0.5–1.5), Ca/C ratio (0–0.6), and other parameters increase, the gas composition shows a gradual increase in the volume content of H2, a gradual decrease in the volume content of CO, and an initial increase and subsequent decrease in the volume content of CH4. Within the range of operating conditions in this study, the optimal conditions for producing hydrogen-rich gas are 700 °C, an S/B ratio of 1.5, and a Ca/C ratio of 0.6. Furthermore, increasing the height of the material layer in the gasification furnace (residence time) enhances the absorption of CO2 by the calcium absorbents, thus promoting an increase in the volume content of H2 and the carbon conversion rate in the gas.

Cavitation damage inducing the improvement of jet breaking efficiency during hydrate drilling

Natural gas hydrate (NGH) is an environment-friendly energy source with great development potential. Cavitation jet is a promising technology to improve drilling rate for both the solid fluidization method and integrated method of radial jet drilling and completion. This work aims at the improvement of jet breaking efficiency and thereby the NGH production. Firstly, gas hydrate-bearing sediments (GHBS) samples are synthesized in laboratory, and the erosion tests are conducted with the conical jet (CJ) and convergent-divergent cavitation jet (CDCJ). Then, the distribution characteristics of velocity, cavitation and pressure are simulated in CJ and CDCJ flows. Finally, the collapse behaviours of a single cavitation bubble near a hydrate surface are investigated to preliminarily identify the responsible cavitation damage mechanisms. Results indicate that the CDCJ shows stronger reaming effect and performance of hole depth extension. Under the present hydraulic conditions, the CDCJ increases the erosion pit volume by 30% and saves the specific energy by 23%. The cavitation damage along the hydrate wall can be produced by the combination of impulse pressure and thermal damage. This study reveals the effect of cavitation damage on GHBS and presents preliminary insights into the potential application of cavitation jets in NGH production.

On the cavity flow of a cylinder exiting water obliquely

The water exit of a high-speed cavitation vehicle is a highly complex problem. Especially when the vehicle exits the water at different angles, the cavity shape and motion stability are affected by the air-water interface, resulting in significant changes in the mechanical environment and dynamics of the vehicle during the water exit. To solve this problem, a CFD method based on VOF multiphase flow interface-capturing technique and overset mesh technique is adopted to numerically calculate the interaction of vapor-liquid-air multiphase flow during the oblique water exit of a high-speed cylinder. Based on the verification of the computational model by mesh convergence and water-entry experiment, the cavitation evolution and flow distribution characteristics of the high-speed cylinder during oblique water exit is analyzed. Moreover, the effects of water-exit angles on the surface pressure distribution and drag characteristics of the cylinder are studied. The results show that the fluid at the end of the cavity impacts the shoulder of the cylinder during oblique water exit, resulting in the pressure difference between the upper and lower surfaces of the cylinder, which may finally leads to motion deviation. With the decreasing water-exit angle, the negative peak drag coefficient decreases while the peak lateral force coefficient increases, and there is a critical range of water-exit angel for lateral force and pitch angle variation.

Blade reduced model considering local contact and analyzing blade vibration characteristics

A dynamic model of a tenoned rotating blade considering the pressure distribution characteristics of the contact interface is established and the degree of freedom of the model is reduced by the double coordination free-interface modal synthesis method in this paper. Firstly, the finite element model of the blade is established by ANSYS and the finite element matrix is extracted. Subsequently, multiple contact pairs were established on the contact surface of the tenon to capture the micro-slip characteristics of the contact interface. The normal pressure of the contact pair is obtained by the ANSYS blade-disk contact prediction and load equivalence to take the pressure distribution characteristics into account in the blade dynamics analysis. Then, non-uniform aerodynamic excitation is applied to the blade to simulate the load on the blade under real working conditions. Finally, the double coordination free-interface modal synthesis method is used to reduce the degree of freedom. Due to the coordination condition of the force and displacement of the substructure connection interface, the degree of freedom of the substructure interface is directly reduced. The final reduced degree of freedom is only the sum of the retained modes of the substructure, which greatly improves the computational efficiency. The dynamic equation is solved by the time integration method, and the effects of the tenon angle, rounded corner, and friction coefficient are discussed. The results show that the double coordination free-interface modal synthesis method can greatly reduce the degree of freedom of the tenon-connected blade model under the premise of ensuring accuracy while retaining the local contact characteristics of the contact interface. The structural parameters of the dovetail structure have a great influence on the vibration reduction characteristics of the blade. When designing the tenon structure, it is necessary to pay attention to these parameters.

Wind field and pressure characteristics on wind turbine surface under moving thunderstorms

Based on computational fluid dynamics and large-eddy simulation technologies, a numerical simulation method of a moving thunderstorm field is established by considering the impinging jet model. In addition, the influence of movement speed of the storm center and jet velocity changes on the characteristics of the wind field is presented. By drawing horizontal wind speed radial profile curves, the vertical profile curves of horizontal wind velocity, radial wind profile curves of vertical wind speed, and transient wind speed characteristics of a moving thunderstorm downburst are illustrated. The results demonstrate that the wind field of a moving thunderstorm exhibits clear asymmetric characteristics. As the height from the ground increases, the horizontal wind speed first increases and then decreases. The extreme value of the horizontal wind speed appears at the position of (0.01–0.03) Djet (where Djet is the jet spout diameter) near the ground, which is consistent with the characteristics of a static thunderstorm wind field. Simultaneously, the distribution characteristics of wind pressure on the surface of wind turbines under moving thunderstorms is further studied. By considering variations of the wind attack angle, jet velocity, and moving speed, the results of wind pressure on the tower and blades of the wind turbine are presented. The coupling of the moving speed and jet velocity has a significant influence on the wind field and pressure on the wind turbine surface.

Flow characteristic investigation on Laval-type flow rate regulating valves by fluid-thermal-structure interaction

The flow characteristics are of great significance for flow rate regulating valves (FRRVs) to regulate the mass flow rate of gas and avert excessive energy consumption. Nevertheless, the deformation of fluid-thermal-structure interaction (FTSI) is an impact factor affecting the flow characteristics, which is usually neglected by convention numerical calculations, but can be captured by FTSI numerical calculations. In this work, the Laval structure is proposed to improve the flow characteristics of FRRVs. Numerical studies of FTSI and convention are performed to analyze the flow characteristics of the valve. Based on these numerical calculations, the pressure and velocity distribution characteristics are presented and the temperature, stress, heat exchange, and deformation of FTSI are analyzed. Meanwhile, characteristics of mass flow rate with pressure are evaluated by linear fitting method, and the polynomial fitting method is utilized to capture the characteristics of mass flow rate with valve spool opening. Experimental investigations are also carried out for verification. Compared with experimental data, FTSI numerical results show a good agreement with errors less than 4.974% but the convention numerical ones give relatively larger deviations of 20.64%. The results reveal that the proposed FTSI numerical method is more precise and reasonable for predicting the flow characteristics of FRRVs in engineering.

Numerical Study on the Bearing Capacity of Lubricant Film in Journal Bearing with Micro-textured Surface

For studying the hydrodynamic lubrication performance of micro-textured radial journal bearings, a numerical model of hydrodynamic lubrication for journal bearings was established first. Solve the established numerical model using FDM, and the lubricant film pressure distribution and static characteristics of bearings were obtained. Considering the processing cost and feasibility of the processing technology, the cylindrical texture arranged in the radial of the bearing shell surface is applied, the lubricant film thickness equation considering the micro-texture is introduced into the Reynolds equation. According to the height and distribution density of microstructure, the bearing capacity parameters were obtained. The load-carrying capacity of micro structure journal bearing is significantly higher than that of plain bearing. In this paper, a practical model with cylindrical micro-textured surface is given for journal bearing applications with high capacity demand.

Experimental study on fluctuating aerodynamic force and wind pressure distribution characteristics of three circular cylinders arranged inline

The fluctuating aerodynamic force and wind pressure distribution characteristics of three equally spaced circular cylinders arranged inline at different incidence angles and spacing ratios were studied via rigid model pressure measurement wind tunnel tests. The results were compared with those of a single cylinder. The Reynolds number is 6.4 × 104. The range of incidence angle α and spacing ratio L/D (the ratio of the center distance between adjacent cylinders to the diameter of the cylinder) are 0°∼90° and 1.2 ∼ 4.0, respectively. The spacing ratio and incidence angle greatly influence the fluctuating aerodynamic force coefficients and wind pressure coefficients. According to the spacing ratio, the fluctuating aerodynamic characteristics can be roughly divided into three states: small spacing ratios (1.2 ≤ L/D ≤ 2.0), medium spacing ratios (2.0 < L/D < 3.5), and large spacing ratios (3.5 ≤ L/D ≤ 4.0). The interference effect in the fluctuating aerodynamic force and wind pressure coefficients in the three states is discussed. At small spacing ratios, the fluctuating aerodynamic force and wind pressure coefficients mainly experience a significant reduction effect. At medium and large spacing ratios, the interference effect is closely related to the incidence angle and spacing ratio.

In-situ characterization method for tool ultrasonic vibration in rotary ultrasonic machining based on radiated acoustic pressure

In order to be used in the CNC machining center, one rotary ultrasonic machining (RUM) system needs to adapt to various cutting tools. Corresponding ultrasonic vibration units are often designed to work in a local resonant state rather than a full resonant state due to the diversity and complexity of tool shapes. Since the frequency at which the vibration of various cutting tools reaches the maximum is probably different, it is necessary and important to in-situ determine the working frequency of cutting tools in RUM. The key to determining working frequency is to characterize the tool vibration. Although the existing optical and electrical methods have been widely used for tool vibration characterization in some scenarios, they still have obvious limitations when applied to in-situ characterization in RUM systems. In this context, an in-situ characterization method for the tool ultrasonic vibration based on radiated acoustic pressure is presented in the paper. Firstly, characteristics of acoustic pressure distributions radiated from typical cutting tools in RUM are comprehensively studied based on analytical analysis, numerical simulation, and experimental measurement. Secondly, based on the relationship between the acoustic pressure and tool vibration, the measurement strategy and corresponding in-situ measurement system for acoustic pressure are developed to characterize the tool vibration in RUM. Finally, a series of experiments are conducted by using the measurement system, including determining the working frequency of cutting tools and quantitatively describing the vibration amplitude in RUM. It is shown that the proposed method is efficient and cost-effective for the in-situ characterization of the ultrasonic vibration of various cutting tools in RUM, especially for complexly shaped tools working in a local resonant state.

New Two-BWT Blade Aerodynamic Design and CFD Simulation

Due to reduced manufacturing, transportation, and installation costs, the two-blade wind turbines (Two-BWT) are a viable option for offshore wind farms. So far, there is no mature design model for offshore Two-BWT. This paper proposes an aerodynamic design method for offshore Two-BWT blades using the blade element momentum (BEM) theory. This method calculates the power coefficient of the Two-BWT by analogy with the three-blade wind turbines (Three-BWT), and then determines the wind rotor diameter. Then, the airfoil, chord length, and twist angle are taken as the key design factors. Furthermore, the piecewise combination method (PCM) for airfoil distribution, the three-point sine method (Three-PSM) for chord length distribution, and the two-point sine method (Two-PSM) for torsion angle distribution are adopted, respectively. Subsequently, the minimum rotational speed, under the rated wind speed and rated power, is taken as the optimization objective to establish the optimization model. The global flow field of Two-BWT is constructed based on CFD technology, and the characteristics of wind speed distribution and blade pressure distribution in the flow field are investigated. Finally, the CFD results are compared with the results of the BEM theory, and the consistency of the results also shows the feasibility of the design method.

A comparative study of structural parameters for spiral groove bearing in centrifugal rotary blood pump

In this work, the hydrodynamic characteristics of spiral groove bearing in centrifugal rotary blood pump is investigated for the cases with different structural parameters. The simulation model is proposed based on the CFD technology and the effectiveness of simulation model is demonstrated by the published data. Then, the pressure, load carrying capacity and friction torque are calculated and the characteristics of pressure distribution are analyzed. It is found that the structural parameters of spiral groove would lead to the complex pressure distribution of blood film and the load carrying capacity also changes at the same time. Moreover, the deep analysis of structural characteristics for spiral groove bearing is conducted based on the orthogonal design method, which could improve the computational efficiency of hydrodynamic behavior of spiral groove bearing. And, the mapping relationship between structural parameter and hydrodynamic performance of bearing preferably is also illustrated.

Design and Fabrication of Automated Air Conveyor

Abstract: An automated air conveyor system was developed for transporting objects. The air conveyor forms a thin film underneath the object for support and simultaneously generates a controlled airflow that results in viscous traction. It is potentially applicable in the manufacturing process for semiconductor wafer or flat foodstuffs, where mechanical contact is expected to be avoided during transportation of the products to minimize contamination. The air conveyor employs duplicated arrays of actuating cells that are square pockets with a surrounding dam. A simple model is proposed to characterize the viscous force. The theoretical analysis reveals that the total force is the composition of an actuating force generated in the pocket areas and the side areas and a drag force generated in the dam areas. Experimental investigations are conducted on the basic characteristics of the film pressure distribution and the viscous force. The results show that the air film pressure is symmetrically distributed in the width direction but non symmetrically distributed in the length direction. The viscous force increases if the suction flow rate is enlarged or the gap thickness is narrowed.. Amplitude of the actuating force is adjusted using a control valve to vary the suction flow rate. The simulated and the experimental results verify the feasibility of the air conveyor system and the control method.

Influence of Support Parameter and Excavation Methods on Statistical Distribution Characteristics of Surrounding Rock Pressure in Shallow-Buried Metro Tunnel

For large-spanshallow-buried tunnels in composite strata of urban metro, the study on the distribution characteristics of surrounding rock pressure is a necessary prerequisite for the reliability analysis of tunnel structure. In this paper, through numerical simulation, the random joint file generated by MATLAB is combined with the discrete element software to establish the corresponding random network model. According to the network model calculation, the influence of surrounding rock pressure on the support structure system is discussed, and the reasonable support parameter types are given. Comparing the whole section excavation with the subsectional excavation, the subsectional excavation can effectively control the internal stress self-adjustment of the surrounding rock and effectively restrain the plastic zone. It provides some theoretical guidance and reference for tunnel reliability design.