A Rapid Analysis Tool for Aerodynamics/Aerothermodynamics of Hypersonic Vehicles

A rapid engineering surface panel method to analyze aerodynamics and aerothermodynamics of hypersonic vehicles is developed.To obtain the surface pressure distribution of a hypersonic vehicle,the local surface inclination method is applied to calculate the pressure coefficient for each surface panel element,of which the normal vector is corrected first by using an efficient data structure and Rey-casting algorithm,local Reynolds numbers are calculated according to the geometric streamline method,then the aerodynamic heating flux is computed by both reference enthalpy relations and Reynolds analogy method.Several typical test cases are performed and the results indicate that,the developed tool is effective in predicting the aerodynamics/aerothermodynamics for complex geometry of hypersonic vehicle in a wide range of Mach numbers with a sufficient accuracy.

Adding-Point Strategy for Reduced-Order Hypersonic Aerothermodynamics Modeling Based on Fuzzy Clustering

Reduced order models（ROMs） based on the snapshots on the CFD high-fidelity simulations have been paid great attention recently due to their capability of capturing the features of the complex geometries and flow configurations. To improve the efficiency and precision of the ROMs, it is indispensable to add extra sampling points to the initial snapshots, since the number of sampling points to achieve an adequately accurate ROM is generally unknown in prior, but a large number of initial sampling points reduces the parsimony of the ROMs. A fuzzy-clustering-based adding-point strategy is proposed and the fuzzy clustering acts an indicator of the region in which the precision of ROMs is relatively low. The proposed method is applied to construct the ROMs for the benchmark mathematical examples and a numerical example of hypersonic aerothermodynamics prediction for a typical control surface. The proposed method can achieve a 34.5% improvement on the efficiency than the estimated mean squared error prediction algorithm and shows same-level prediction accuracy.

Simulation of aerothermodynamics model on ballistic safety of fusible alloy fuze

In order to ensure the ballistic safety of fusible alloy fuze at reliable delay arming, melting point of fusible alloy needs to be calculated based on projectile velocity at safe time and distance. Taking shrapnel KZVD fuze of Switzerland oerlikon 2ZLa/353 35 mm double barrel self-propelled antiaircraft artillery as an example, based on the aerodynamics heating theory, the calculation of theory model and simulation of projectile head stagnation point temperature were done in initial stage of sim-plified exterior ballistic from engineering viewpoint when the initial projectile velocity was 1 175 m/s and the error was ±15 m/s. The melting point of fusible alloy in the safe distance was obtained by analyzing the temperature of projectile head stagnation point at corresponding projectile velocity. The simulated results indicate that the melting point of fusible alloy de-rived by theoretical calculation is identical with the result of simulation at the velocity range of 1 160 to 1 190 m/s. So the aero- thermodynamics model can be applied to design the fusible alloy fuze of corresponding melting point based on the requirement of safe distance. This method can be taken as the reference in studying the thermodynamic question of projectile flying at high speed.

A theoretical study on the unsteady aerothermodynamics for attached flow models

The principle of the unsteady aerothermodynamics was theoretically investigated for the attached flow. Firstly, two simplified models with analytic solutions to the N-S equations were selected for the research, namely the compressible unsteady flows on the infinite flat plate with both time-varying wall velocity and time-varying wall temperature boundary conditions. The unsteady temperature field and the unsteady wall heat flux (heat flow) were analytically solved for the second model. Then, the interaction characteristic of the unsteady temperature field and the unsteady velocity field in the simplified models and the effects of the interaction on the transient wall heat transfer were studied by these two analytic solutions. The unsteady heat flux, which is governed by the energy equation, is directly related to the unsteady compression work and viscous dissipation which originates from the velocity field governed by the momentum equation. The main parameters and their roles in how the unsteady velocity field affects the unsteady heat flux were discussed for the simplified models. Lastly, the similarity criteria of the unsteady aerothermodynamics were derived based on the compressible boundary layer equations. Along with the Strouhal number Stu, the unsteadiness criterion of the velocity field, StT number, the unsteadiness criterion of the temperature field was proposed for the first time. Different from the traditional method used in unsteady aerodynamics which measures the flow unsteadiness only by the Stu number, present results show that the flow unsteadiness in unsteady aerothermodynamics should be comprehensively estimated by comparing the relative magnitudes of the temperature field unsteadiness criterion StT number with the coefficients of other terms in the dimensionless energy equation.

Some Aerothermodynamic Aspects of ESA Entry Probes

Two different entry vehicles are presented here： the Inflatable Reentry and Descent Demonstrator （IRDT）, and Huygens. Both missions involve （re）entries at conditions close to orbital, and have been performed in 2005. Specific aspects of the design and the mission of IRDT are briefly outlined. The preliminary results of the recent flight of IRDT and the methodology followed at ESTEC for the assessment of radiative fluxes for Huygens are summarised.

Convergence proof of the DSMC method and the Gas-Kinetic Unified Algorithm for the Boltzmann equation

This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.

Effect of Squealer Tip with Deep Scale Depth on the Aero-thermodynamic Characteristics of Tip Leakage Flow

In this paper,the aero-thermal performance of squealer tips with deep-scale depth is numerically investigated in an axial flow turbine,which is compared with the squealer tip with traditional cavity depth.Numerical methods were validated with experimental data.The effect of cavity depth and tip clearance was considered.The numerical results show that for the squealer tip with conventional cavity depth,the size of the reflux vortex enlarges as the cavity depth increases.The velocity and uniformity of high entropy production rate(EPR)inside the cavity reduce obviously with the cavity developing into deep-scale.However,the increase of depth 10%of the blade span(H)leads to enlargement of cavity volume,which increases the total entropy production rate.And the overall dimensionless entropy production rate(DEPR)of gap and cavity obtains a maximum increase of 43.54%in contrast to the case with 1%H depth cavity.As a result,the relative leakage mass flow rate reduces by 20.6%as the cavity depth increases from 1%to 10%.Given the heat transfer,as the cavity significantly increases to 10%H,the enhanced cavity volume results in a more enormous cavity vortex with low velocity covering the floor,which weakens the convective heat transfer intensity and reduces the area of high heat transfer.The normalized average heat transfer coefficient at the cavity bottom reduces by 40.26%compared to the cavity depth of 1%H.In addition,the deep-scale cavity is more effective in inhibiting leakage flow at smaller tip clearance.The reduction amplitude of normalized average heat transfer coefficient at the squealer floor decreases as tip clearance increases,which reduces at most by about 72.6%for the tip clearance of 1%H.

On the calculation of the electron temperature flowfield in the DSMC studies of ionized re-entry flows

Currently available procedures of electron temperature calculations in studying ionized flows around reentry spacecraft by the direct simulation Monte Carlo(DSMC)method are analyzed.It is shown that the heat conduction of electrons is not taken into account in these procedures.The contributions of various effects to the electron energy balance are calculated by an example of the RAM-C II capsule,and a numerical solution of the electron energy conservation equation is obtained,which refines the electron temperature distribution used in the DSMC computations.A method of coupled calculation of the electron temperature within the framework of the continuum approach and modelling of ionized gas flow by the DSMC method is proposed.

PSEUDOSTREAM FUNCTION FORMULATION——A METHOD OF SOLVING THREE-DIMENSIONAL AERODYNAMIC ANALYSIS AND DESIGN PROBLEMS IN TURBOMACHINERY

In this paper two pseudostream functions are defined in view of the characteristic featuresof the momentum equations and the requirement of continuity. The principal equationsof eiher pseudostream functions only contain the terms of its own second-order partial deriv-atives and do not include those of the other, and these equations can be easily solved. Theentire three-dimensional solution is then obtained through solving the principal equations ofboth pseudostream functions separately and iterating the two solutions. The principal equa-tions of the pesudostream functions in a nonorthogonal curvilinear coordinates and thecorresponding boundary conditions are given. The three-dimensional aerothermodynamicanalysis problem and design problem are discussed, some calculations are conducted and theresults are compared with the analytical solution and with that of other methods. It is seenthat this method is accurate in theory and simple in computation, and may be widely usedin three-dimensional flow calculations.

A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD

Aerothermoelasticity is one of the key technologies for hypersonic vehicles. Accurate and efficient computation of the aerothermodynamics is one of the primary challenges for hypersonic aerothermoelastic analysis. Aimed at solving the shortcomings of engineering calculation, compu- tation fluid dynamics （CFD） and experimental investigation, a reduced order modeling （ROM） framework for aerothermodynamics based on CFD predictions using an enhanced algorithm of fast maximin Latin hypercube design is developed. Both proper orthogonal decomposition （POD） and surrogate are considered and compared to construct ROMs. Two surrogate approaches named Kriging and optimized radial basis function （ORBF） are utilized to construct ROMs. Furthermore, an enhanced algorithm of fast maximin Latin hypercube design is proposed, which proves to be helpful to improve the precisions of ROMs. Test results for the three-dimensional aerothermody- namic over a hypersonic surface indicate that： the ROMs precision based on Kriging is better than that by ORBF, ROMs based on Kriging are marginally more accurate than ROMs based on POD- Kriging. In a word, the ROM framework for hypersonic aerothermodynamics has good precision and efficiency.

Aerodynamic design,analysis,and validation techniques for the Tianwen-1 entry module

The clear differences between the atmosphere of Mars and the Earth coupled with the lack of a domestic research basis were significant challenges for the aerodynamic prediction and verification of Tianwen-1.In addition,the Mars entry,descent,and landing(EDL)mission led to specific requirements for the accuracy of the aerodynamic deceleration performance,stability,aerothermal heating,and various complex aerodynamic coupling problems of the entry module.This study analyzes the key and difficult aerodynamic and aerothermodynamic problems related to the Mars EDL process.Then,the study process and results of the design and optimization of the entry module configuration are presented along with the calculations and experiments used to obtain the aerodynamic and aerothermodynamic characteristics in the Martian atmosphere.In addition,the simulation and verification of the low-frequency free oscillation characteristics under a large separation flow are described,and some special aerodynamic coupling problems such as the aeroelastic buffeting response of the trim tab are discussed.Finally,the atmospheric parameters and aerodynamic characteristics obtained from the flight data of the Tianwen-1 entry module are compared with the design data.The data obtained from the aerodynamic design,analysis,and verification of the Tianwen-1 entry module all meet the engineering requirements.In particular,the flight data results for the atmospheric parameters,trim angles of attack,and trim axial forces are within the envelopes of the prediction deviation zones.