An experimental study of the influence of spike in supersonic and transonic flows past a hemispheric body

Snažan udarni talas, koji nastaje pri nadzvučnom letu projektila zaobljenog vrha, značajno povećava njegov otpor i aerodinamičko zagrevanje. Oba efekta mogu da se umanje montiranjem igle na vrh projektila. Osim postojanja same igle, i njena dužina i oblik takođe mogu da utiču na aerodinamičke karakteristike zaobljenog tela. Ovaj rad prikazuje eksperimentalne rezultate uticaja oblika igle na aerodinamičke koeficijente sila i momenata, kao i na poziciju centra pritiska, pri nadzvučnom i okolozvučnom opstrujavanju modela projektila polusfernog vrha. Eksperiment je izveden u trisoničnom aerotunelu pri Mahovim brojevima M =1,89 i M =1,03 i različitim napadnim uglovima (0○ -10○ ). Vizualizacija strujnog polja pri nadzvučnom opstrujavanju modela izvedena je šliren metodom. Ona je omogućila kvalitativnu analizu strujnog polja vazduha oko modela bez igle i modela sa četiri igle različitog oblika. Na osnovu vizualizacije strujnog polja izvedeni su zaključci koji su u skladu sa dobijenim brojnim vrednostima aerodinamičkih koeficijenata. Eksperimenti pokazuju da igla i njen oblik imaju uticaja samo pri nadzvučnom letu projektila, dok igla ne utiče, ili čak malo pogoršava aerodinamičke karakteristike projektila pri okolozvučnom letu. Dobijeni rezultati se mogu šire primeniti, na primer pri projektovanju supersoničnih letilica.A strong shock wave during a supersonic flight of a blunt-nosed projectile increases the drag and aerodynamic heating considerably. A spike can be mounted on the nose of the projectile to reduce these effects. Apart from its very existence and its length, the spike's shape may also affect the aerodynamic characteristics of a blunt body. This paper presents the results of an experiment that analyzed the influence of the spike's shape on the aerodynamic forces and moments coefficients, and the location of the center of pressure, at supersonic and transonic flows past a model of a projectile with a hemispheric forebody. The experiment was carried out in a trisonic wind tunnel, for Mach numbers M=1.89 and M=1.03 and different angles of attack (0○ -10○ ). Visualization of the experiments was performed by the schlieren method in the case of supersonic flow. It enables qualitative analysis of the airflow around the tested model without and with four different spikes. The conclusions are by the obtained values of the aerodynamic coefficients. The experiments show that a spike and its shape affect only the performance of the tested projectile during its supersonic flight. Besides, a spike does not affect or even slightly impairs the aerodynamic performance of the projectile during its transonic flight. The obtained results are applicable in broader contexts, e.g. for the design of an aircraft for supersonic flights

Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow

The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number (Kn lt = 0.1), i. e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy

Influence of transport coefficients' dependence on temperature for gas flow in microbearing

The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn lt = 10(-1)) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected

A constant wall temperature microbearing gas flow

U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja.A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained

A microbearing gas flow with different walls' temperatures

An analytical solution for the non-isothermal 2-D compressible gas flow in a slider microbearing with different temperatures of walls is presented in this paper. The slip flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3-10-1, which corresponds to the slip flow. The ratio between the exit microbearing height and the microbearing length is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of rarefaction effect. The analytical solutions of the pressure, velocity, and temperature for moderately high Reynolds numbers are presented here. For these flow conditions the inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid are presented in the second approximation, also

Microchannels and Nanochannels Gas Flow for the Entire Knudsen Number Domain

This paper presents an analytical solution for steady rarefied compressible viscous gas flow in the microchannels and nanochannels with constant or slowly varying cross section. It covers both all gas rarefaction regimes (from continuum to free molecular gas flow) and all Mach number regimes (from subsonic to supersonic). The solutions for the velocity and pressure distribution in the channels is obtained by the macroscopic approach, using the one-dimensional model of continuum equations. A specially modeled friction factor is attained by an approach that includes both the general velocity slip boundary condition, and the dynamic viscosity generalized by the rarefaction correction parameter. This method spreads the application of the solution to the entire range of Knudsen numbers. Moreover, inclusion of the inertia effect into the governing equations allows the application of the solution to both subsonic and supersonic gas flows. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging and microchannels and nanochannels with constant cross section

Rarefied gas flow in microtubes at low Reynolds numbers

U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora.Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable

Rarefied gas flow in microtubes at low Reynolds numbers

U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora.Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable