The Estimation of the Non-Linear Lift of Delta Wings at Supersonic Speeds

1963 ◽  
Vol 67 (632) ◽  
pp. 476-480 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Mathematical Model ◽  
Linear Theory ◽  
Free Stream ◽  
Separated Flow ◽  
Leading Edge ◽  
Delta Wings ◽  
Non Linear ◽  
Leading Edges ◽  
The Mathematical Model ◽  
Slender Wing

Summary:Up to the present most of the methods used to calculate the flow over delta wings with leading edge separations have been based on slender wing theory. In this paper one of the simplest of these methods is carried over to linear theory and the overall lift calculated. In general the results are in agreement with experiment, in particular both show a fall in nonlinear lift as the leading edges of the wing approach the free stream Mach angles. The discrepancies which exist appear to arise mainly from the use of linear theory rather than from the mathematical model introduced to treat the separated flow.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Separated Flow Past a Slender Delta Wing at Incidence

1973 ◽  
Vol 24 (2) ◽  
pp. 120-128 ◽  
Author(s):  
J E Barsby
Keyword(s):  
Delta Wing ◽  
Separated Flow ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Simultaneous Equations ◽  
Delta Wings ◽  
Nested Iteration ◽  
Finite Difference Technique ◽  
Flow Past ◽  
Vortex Systems

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

Boundary layer development after a separated region

1998 ◽  
Vol 374 ◽  
pp. 91-116 ◽  
Author(s):  
IAN P. CASTRO ◽  
ELEANORA EPIK
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Turbulence Models ◽  
Separated Flow ◽  
Leading Edge ◽  
Turbulence Structure ◽  
Outer Flow ◽  
Free Stream Turbulence ◽  
Layer Region

Measurements obtained in boundary layers developing downstream of the highly turbulent, separated flow generated at the leading edge of a blunt flat plate are presented. Two cases are considered: first, when there is only very low (wind tunnel) turbulence present in the free-stream flow and, second, when roughly isotropic, homogeneous turbulence is introduced. With conditions adjusted to ensure that the separated region was of the same length in both cases, the flow around reattachment was significantly different and subsequent differences in the development rate of the two boundary layers are identified. The paper complements, but is much more extensive than, the earlier presentation of some of the basic data (Castro & Epik 1996), confirming not only that the development process is very slow, but also that it is non-monotonic. Turbulence stress levels fall below those typical of zero-pressure-gradient boundary layers and, in many ways, the boundary layer has features similar to those found in standard boundary layers perturbed by free-stream turbulence. It is argued that, at least as far as the turbulence structure is concerned, the inner layer region develops no more quickly than does the outer flow and it is the latter which essentially determines the overall rate of development of the whole flow. Some numerical computations are used to assess the extent to which current turbulence models are adequate for such flows.

Model and Parameters Identification of Non-Linear Joint by Force-State Mapping in Frequency Domain

2007 ◽  
Vol 23 (4) ◽  
pp. 367-380 ◽  
Author(s):  
J.-H. Wang ◽  
H.-Y. Huang
Keyword(s):  
Mathematical Model ◽  
Frequency Domain ◽  
Measurement Data ◽  
Optimal Model ◽  
Identification Procedure ◽  
Non Linear ◽  
Allowable Range ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Nonlinear Joints

AbstractGenerally, the Force-State Mapping (FSM) is an effective method to identify the parameters of nonlinear joints provided that the joint model is exactly known in advance. However, the variation of the non-linear joints is so large that the mathematical models of non-linear joints generally are not known in advance. Therefore, the model and the parameters of a non-linear joint should be identified simultaneously in practice. In this work, a new identification procedure which was based on the FSM method in frequency domain was proposed to identify the mathematical model and parameters of a non-linear joint simultaneously. Generally, there are many feasible combinations of models and parameters which can satisfy the measurement data within an allowable range of error. In this work, an iteration procedure was used to update the feasible models to result in an optimal model with its parameters. The simulation results show that a proper mathematical model and accurate parameters can be identified simultaneously by the new procedure even that the measurement data are contaminated by noise.

Vortex Breakdown Effects on the Low-speed Aerodynamic Characteristics of Slender Delta Wings in Symmetrical Flow

1967 ◽  
Vol 71 (676) ◽  
pp. 319-322 ◽  
Author(s):  
D. Hummel ◽  
P. S. Srinivasan
Keyword(s):  
Vortex Breakdown ◽  
Vortex Formation ◽  
Vortex Sheet ◽  
Aerodynamic Characteristics ◽  
Flow Visualisation ◽  
Delta Wings ◽  
Vortex Sheets ◽  
The Core ◽  
Leading Edges ◽  
Slender Wing

Even at small angles of incidence, the flow separates from the sharp leading edges of a slender wing. These flow separations usually lead to the formation of two free vortex layers, joined to the leading edges of the wing and rolling up to form spiral-shaped vortex sheets above the upper surface of the wing. This vortex formation is illustrated schematically in Fig. 1. The streamlines on the vortex sheet follow helical paths. Smoke injected near the wing apex for flow visualisation remains concentrated close to the axis of the core of the vortex sheet.

Boundary layer receptivity to free-stream sound on elliptic leading edges of flat plates

2001 ◽  
Vol 429 ◽  
pp. 1-21 ◽  
Author(s):  
JUAN B. V. WANDERLEY ◽  
THOMAS C. CORKE
Keyword(s):  
Flat Plate ◽  
Acoustic Waves ◽  
Free Stream ◽  
Stokes Equations ◽  
Leading Edge ◽  
Neutral Curve ◽  
Curvilinear Coordinates ◽  
Flat Plates ◽  
Linear Superposition ◽  
Leading Edges

The leading-edge receptivity to acoustic waves of two-dimensional bodies is investigated using a spatial solution of the Navier–Stokes equations in vorticity/stream function form in general curvilinear coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998), in which the solution for the basic flow and the linearized perturbation flow are solved separately. The initial motivation for the work comes from past physical experiments for flat plates with elliptic leading edges, which indicated narrow frequency bands of higher neutral-curve Branch I receptivity. We investigate the same conditions in our simulations, as well as on a parabolic leading edge. The results document the importance of the leading edge, junction between the ellipse and flat plate, and pressure gradient to the receptivity coefficient at Branch I. Comparisons to the past experiments and other numerical simulations showed the influence of the elliptic leading-edge/flat-plate joint as an additional site of receptivity which, along with the leading edge, provides a wavelength selection mechanism which favours certain frequencies through linear superposition.

Non-Linear Analysis of Plethysmograms and the Effect of Communication on Dementia in Elderly Individuals

2011 ◽  
pp. 192-198
Author(s):  
Mayumi Oyama-Higa ◽  
Tiejun Miao ◽  
Yoko Hirohashi ◽  
Yuko Mizuno-Matsumoto
Keyword(s):  
Mathematical Model ◽  
Communication Skills ◽  
Linear Analysis ◽  
Conclusive Evidence ◽  
Elderly Individuals ◽  
Non Linear ◽  
Pulse Waves ◽  
Severity Of Dementia ◽  
The Mathematical Model ◽  
The Brain

The authors of this chapter measured plethysmography and calculated the Largest Lyapunov Expornent (LLE) using non-linear analysis. They found that the value of LLE was significantly related to the severity of dementia and the communication skill in the ADL index for 144 elderly individuals. The authors developed a mathematical model to analyze the results by studying the information extracted from the plethysmogram data. Furthermore, data were collected when the central nerve was blocked by general anesthesia to evaluate the mathematical model. The pulse wave data indicated that the authors included information from the nucleus of the brain origin. In other words, they obtained conclusive evidence of dementia using the LLE and communication skills. The authors measured pulse waves while elderly individuals had a conversation. They calculated the activation of the sympathetic nerve and the parasympathetic (LF/HF, HF) response simultaneously. LLE that was activated by communication had a low HF, and the HF was high in individuals who were not activated. In other words, an effect of communication was observed in conscious elderly individuals. Communication scientifically indicated the mental activity of elderly individuals.

Computation of Separated-Flow Transition Using a Two-Layer Model of Turbulence

1999 ◽  
Vol 121 (1) ◽  
pp. 78-87 ◽  
Author(s):  
E. L. Papanicolaou ◽  
W. Rodi
Keyword(s):  
Free Stream ◽  
Separated Flow ◽  
Leading Edge ◽  
Expansion Ratio ◽  
Turbulence Level ◽  
Layer Model ◽  
Practical Applications ◽  
Free Stream Turbulence ◽  
First Case ◽  
Two Layer Model

A model for predicting transition in flows with separation is presented in this study. The two-layer model of turbulence is employed, along with a suitably defined intermittency function, which takes appropriate values in the laminar-, transitional- and turbulent-flow regions. Correlations derived from measurements are used for this purpose. Two test cases were selected: the flow over a long horizontal body with semi-circular leading edge and the flow over the backward-facing step of small height (expansion ratio of 1:1.01). In the former, oncoming flows with a free-stream turbulence level encountered in practical applications was considered (0.2–5.6 percent) whereas in the latter the corresponding level was much lower. The Reynolds numbers, based on the diameter in the first case and on the step height in the second, lie in the range of 1600–6600, in which limited numerical investigations were previously available and where bubbles with laminar separation and turbulent reattachment are expected. The predictions were found to compare well with the corresponding measurements, both in terms of the lengths of the separation and the transition regions and of velocity and turbulence intensity profiles at various stream-wise locations. The results show that, for the transition criterion chosen, in all cases transition is completed downstream of the reattachment point and that the rate at which it is completed increases with the free-stream turbulence level.

Sign in / Sign up

Export Citation Format

Share Document